Modelling the spread of Middle East respiratory syndrome coronavirus (MERS-CoV) in Saudi Arabia

Qianying Lin, Alice P.Y. Chiu, Shi Zhao and Daihai He∗ Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong (SAR) China * [email protected]

October 31, 2017

1 Abstract

2 Middle East Respiratory Syndrome Coronavirus (MERS-CoV) has been persistent in

3 the Middle East region since 2012. Abundant scientific evidence showed that dromedary

4 camels are the primary host of the virus. Majority of human cases (i.e. 75% or 88%) are

5 due to human-to-human transmission, while the others are due to camel-to-human transmis-

6 sion. Mathematical modelling of MERS-CoV camel-to-camel transmission was lacking. Us-

7 ing the plug-and-play likelihood-based inference framework, we fitted a susceptible-exposed-

8 infectious-recovered-susceptible model of camels to the reported human cases with a constant

9 proportion of human cases from camels (i.e. either 25% or 12%). We considered two scenarios:

10 (i) the transmission rate among camels is time-varying with a constant spill-over rate from

11 camels to human, or (ii) the spill-over rate is time-varying with a constant transmission rate

12 among camels. Our estimated loss-of-immunity rate and prevalence of MERS-CoV infections

13 among camels largely matched previous serological or virological studies, shedding light on

14 this issue. We recommended including dromedary camels in animal surveillance and control of

15 MERS-CoV in Saudi Arabia which could help reduce their sporadic introductions to humans.

16 Introduction

17 Since the first human case of Middle East respiratory syndrome coronavirus (MERS-

18 CoV) infection, identified in Jeddah, Saudi Arabia in September 2012, 2,040 laboratory-

19 confirmed cases, including 712 deaths, have been reported in 27 countries as of July 12, 2017

20 [1]. The virus circulated in the Arabian Peninsula, particularly in Saudi Arabia. In May

21 2015, the Republic of Korea reported the largest outbreak outside the Middle East region.

22 Many external factors could possibly impact the transmission of MERS-CoV among

23 camels and human. In particular, Hajj and Umrah are two annual religious festivals that

24 attract more than 10 million pilgrims from 184 countries to Saudi Arabia. Hajj is considered

25 a major pilgrimage and involves mass gathering that lasts for six days during the 12th month

26 of the Islamic calendar each year, while Umrah, a minor pilgrimage which could be highly

1 27 individualized, is made mostly during Ramadan, a period of 29 to 30 days during the 9th

28 month of the Islamic calendar [2]. Several studies have demonstrated that these mass gather-

29 ings, which attracted pilgrims worldwide, were potential for transmission of infectious diseases

30 [3]. Lessler et al. estimated the potential incidence of MERS-CoV among pilgrims attending

31 Hajj in Saudi Arabia in 2014 to be 6.2, 11.7 and 47.6 pilgrims under the expected, high and

32 very high incidence scenarios, respectively [4]. Furthermore, Poletto (2014) suggested that

33 population movement and human mixing, which were common in Hajj and Umrah, played

34 an important role in MERS-CoV transmission [5]. Besides popuation movement and human

35 mixing during religion events, camels racing, close and re-opening of camel market, as well

36 as climatic factors could impact of the transmission of MERS-CoV among camels, spill-over

37 from camels to human and among human.

38 Reproduction number (R), defined as the average number of cases generated by a typical

39 case, quantifies the intensity of transmission [6]. Past research showed substantial variations

40 on the estimate of reproduction number on MERS-CoV epidemic, depending on a number

41 of factors: the specific location (i.e. Middle East region or Republic of Korea), the time

42 period considered, mode of transmission, and the choice of mathematical modeling techniques

43 [5, 7, 8, 9, 10, 11].

44 Chowell et al. developed a dynamic transmission model that distinguished between

45 the different routes of MERS-CoV transmission. They found that zoonotic transmission was 46 much more effective than human-to-human transmission, with their R0 being 0.84 and 0.36, 47 respectively [9]. Breban et al. used Bayesian analysis to estimate the pandemic risk for MERS- 48 CoV. R0 generated for human-to-human transmission under the most pessimistic scenario and 49 the most optimistic scenario were 0.69 and 0.60 respectively. Their study also highlighted

50 the importance of reducing the rate of zoonotic introductions to the human populations

51 [11]. Poletto et al. (2014) used a novel maximum likelihood approach to jointly estimate 52 R0 and the rate of sporadic introduction of MERS-CoV in the Middle East region. They 53 found that R0 was 0.50 and the rate of sporadic introduction was 0.28 case per day [5]. 54 More recently, Poletto et al. (2016) used a stochastic modeling approach combined with

55 analysis of imported cases out of the Middle East region. Their model, which assumed

56 partial information on transmission scenario, was a much better fit than the model that

57 assumed complete information on transmission. Their combined modeling approach was able

58 to show that about 75% of the MERS-CoV cases were human-to-human transmission [10].

59 In other words, primary human cases that are acquired via camels or camel-related products,

60 accounted for 25% of all human cases. Cauchemez et al. (2016) developed a comprehensive

61 statistical framework to analyze the transmission patterns of MERS-CoV among human in

62 Saudi Arabia between January 2013 and July 2014 [12]. They found that the proportion of

63 human cases from the reservoir was 12% (95% CI: 9%, 15%), and they also noted that the

64 ratio could be 17% (95% CI: 13%, 20%) if only restricted to passive surveillance cases only

65 [12]. Kucharski and Althaus (2015) modeled on MERS-CoV transmission in South Korea.

66 Their study showed substantial over-dispersion in transmission, which indicated there was

67 a potential for superspreading of MERS-CoV [7]. Superspreading cases are primary cases

68 which infect disproportionately more secondary contacts than other primary cases of the

69 same disease. Hsieh studied the South Korean MERS-CoV outbreak using a Richard’s model

70 and found that the turning point, which is the peak timing of an epidemic, took place at 23 71 to 24 days after the onset of the index case. The estimated R0 ranged between 7.0 to 19.3

2 72 [8]. All of these modeling studies on MERS-CoV had primarily focused on human cases.

73 In a review article by Zumla et al [13], it was pointed out that camel-to-human transmis-

74 sion could be due to indirect exposure, e.g. patients might be exposed to MERS-CoV virus

75 via consumption of unpasteurized camel milk, a practice which is not uncommon in Saudi

76 Arabia. In a sero-prevalence study of MERS-CoV by Muller et al [14], the percentages of

77 MERS-CoV-antibody positive in the general population, camel shepherds and slaughterhouse

78 workers were found to be 0.15%, 2.3% and 3.6%, respectively. Sero-positive rates exceeding

79 74%, which indicates previous infections, were found among camels in Saudi Arabia and its

80 neighboring countries. The virus isolation rate was also high among camels, exceeding 7%

81 but they vary across localities and are higher among juvenile camels [15, 16, 17, 18, 19, 20].

82 Re-infections of MERS-CoV among camels were also identified [21, 22].

83 In this work, we fit the weekly primary human cases of MERS-CoV with a Susceptible-

84 Exposed-Infected-Recovered-Susceptible (SEIRS) model for the dromedary camel population,

85 with a constant proportion of primary human cases from camels (i.e. either 25% or 12%). We

86 considered two scenarios: (i) the transmission rate among camels is time-varying while the

87 spill-over rate is constant; (ii) the spill-over rate is time-varying while the transmission rate

88 is constant. Our aim is to find out whether simple epidemic models with largely biologically

89 plausible parameters can simulate the epidemics of MERS-CoV among camels. If yes, our

90 objectives are to answer the followings: (i) How prevalent is the MERS-CoV infection among

91 camels? (ii) How fast does the immunity decay among camels? (iii) Do these estimates match

92 those of earlier serological and virological studies?

93 Methods

94 Data

95 We obtained weekly MERS-CoV cases from the EMPRES-i Global Animal Disease

96 Information System [23]. Monthly percentages of MERS-CoV infected camels from May 2014

97 to April 2015 in Saudi Arabia are obtained from Sabir et al. [24].

98 Mathematical Modelling

99 Our mathematical model is a susceptible-exposed-infectious-recovered-susceptible (SEIRS)

100 framework for camel-to-camel transmission. The model structure is depicted in Figure 1.

101 Here, S, E, I and R represent the numbers of susceptible, exposed, infectious and recovered,

102 and C represents the weekly laboratory-based human confirmations. The total population

103 size of dromedary camels, N = S + E + I + R, is assumed to be constant at 270,000 [25, 26]

104 and the study period went from January 1, 2014 to May 31, 2016.

105 The maximum lifespan of dromedary camels in captivity could reach 28.4 years [27].

106 A number of studies showed that calves that are younger than two years old with primary

107 infections were more likely play a stronger epidemiological role in MERS-CoV transmission

108 compared to older camels that are two to four years old. This is because infected calves have

109 frequent viral shedding and demonstrate a lower rate of seroconversion than older camels

110 [28, 29, 30, 31, 32, 33]. Furthermore, a more recent study by Sabir et al. found that the

111 evolution of MERS-CoV has led to diverse lineages, they suggested that dromedary camels

3 112 hosted this recombination event [24]. Thus, we suspect the duration of immunity protection

113 induced by MERS-CoV infection could last for many years. The infectious period for camels

114 was in days [30], and we assume a latent period of two days and an infectious period of four

115 days.

116 We focused on weekly human cases in Saudi Arabia from January 1, 2014 to May 31,

117 2016. In our model (Figure 1), ρ is the spill-over rate between camel cases and primary

118 human cases. We assume that the primary human cases are 1/4 of all human cases in any

119 week, and we consider this ratio to be 12% in the supplementary material. Thus we convert

120 the reported weekly overall human cases to primary human cases by multiplying 1/4 and

121 round all numbers up to the next integer. Thus, we assume each MERS-CoV camel case

122 leads to roughly 4ρ human cases (i.e. both primary and secondary cases). The assumption

123 of 1/4 is due to the observation that 25% of human cases are likely primary cases. A minor

124 change on this primary case ratio (e.g. from 1/4 → 1/2) will change the estimate from ρ → ρ˜,

125 but this will keep their product roughly constant, i.e. 4ρ = 2˜ρ. Also, it will have a minor

126 impact on the overall fitting and other parameter estimates. However, if the primary case

127 ratio is too small, (e.g. 1/4 → 1/10), the estimated primary human cases will become 1 for

128 almost every week due to data transformation, thus we will lose the temporal pattern in the

129 original data. In that case, we need to seriously consider modelling for the human-to-human

130 transmission. In our data, the primary case ratio is not too small, the temporal patterns

131 are largely kept. Human-to-human transmission is limited to close contacts within a hospital

132 ward or a household setting [34], all of which justify our simple transformation.

Figure 1: SEIRS model structure

The model is as follows: S˙ = µN + λR − β(t)SI − µS, E˙ = β(t)SI − σE − µE, (1) I˙ = σE − γI − µI, R˙ = γI − λR − µR.

133 where β(t) is the transmission rate, µ are the natural death and birth rates, N is the population

4 134 size of camels, σ and γ are rates at which infected camels change status from exposed to

135 infectious or from infectious to recovered. Finally, λ is the rate at which recovered camels lose

136 immunity protection due to multiple factors, such as evolution of the virus, [24, 35], natural

137 loss-of-immunity [24, 35]), imports of susceptible juvenile camels and exports or consumption

138 of recovered adult camels [36]. Susceptible camels could also be exported and consumed for

139 meat. We assumed that the replenishment of susceptible camels to be immediate, i.e. the

140 export and consumption of susceptible camels will cancel out with the import of them, and

141 these terms will not appear in the model equations. We also assumed that there is no export

142 or consumption of infectious camels, which is acceptable if the prevalence is less than 10%

143 during the study period. Thus, the model simulated weekly number of primary human cases due to spill-over are: Z Zi = ργIdt (2) week i

where I is the number of MERS-CoV camel cases at any time. We denoted Ci as the observed number of primary human cases in ith week, and we assume it follows Negative-Binomial (NB) distribution (R version 2.15.2)

Ci ∼ NB (mean = Zi, variance = Zi(1 + τZi)) (3)

144 where τ is an over-dispersion parameter which will be estimated. When τ = 0, the NB

145 distribution is reduced to Poisson distribution. The log likelihood function is

n X l(θ) = log f(Ci|C1:i−1, θ) (4) i=1

146 where θ is the set of unknown parameters and f(Ci|C1:i−1, θ) are the conditional densities for 147 Ci given C1:i−1, which will be numerically calculated via Sequential Monte Carlo (see [37]). 148 We use Partially Observed Markov Process (POMP) iterated filtering method [38, 39,

149 40, 41, 42] within a plug-and-play likelihood-based inference framework [37] to generate the

150 maximum likelihood estimates for θ (R Package ‘pomp’ is available at [43]). A tool for max-

151 imum likelihood inference on partially observed dynamical system is the iterated filtering

152 algorithm. For parameter space exploration, stochastic perturbations to the unknown pa-

153 rameters are introduced. Sequential Monte Carlo, i.e. the particle filter, is applied to the

154 extended model and this will result in selection of parameter values that are more consistent

155 with the data. If these procedures are well constructed, then iterated filtering with succes-

156 sively diminished perturbations, will result in the convergence of the maximum likelihood

157 estimate. This approach is non-trivial. It is described in more detail in the Supplementary

158 Materials, technical documentation of R package [43] and wikipedia [44]. Infectious disease

159 modelling studies such as Ebola, cholera, malaria, influenza, pertussis, HIV, measles and polio

160 virus have used this method [44]. The merits of this package are fivefold. (i) Only model sim-

161 ulation is required to compute the likelihood, with only a few lines of C programming codes

162 that describes the model equations; (ii) It can be implemented in the R software package

163 which is freely available, and where C programming codes can be executed; (iii) hidden state

5 164 variables are calculated and are available in the output; (iv) one can assume a parameter to

165 be time-dependent (such as a cubic-spline function of time) and then estimate the flexibility.

166 Flexibility is reflected by the number of nodes, or degrees of freedom, in a time-dependent

167 cubic spline function. If the number of nodes is very large, then the parameters represented by

168 the spline function could change very rapidly over time, or vice versa. This is an advancement

169 compared to previous models where constant parameters (or a particular function, such as an

170 exponential function) were frequently assumed; (v) The POMP package can be run on high

171 performance workstation in a parallel or a serial manner, which makes large-scale modelling

172 selection feasible. POMP is described in more detail in Supplementary Materials S1. Bayesian information criterion (BIC) [45] is used for assessing the performance of dif- ferent models: ˆ BIC = −2l(θ) + Np ln Nd (5)

173 where Nd denotes the number of data points and Np denotes the number of free parameters. 174 We use BIC rather than Akaike Information Criterion because the former generally penalizes

175 free parameters more strongly.

176 We studied the following modelling scenarios: (i) we assumed only transmission rate is

177 time-dependent and the flexibility is determined by BIC; (ii) we assumed only transmission

178 rate is time-dependent without restriction on the flexibility; (iii) we assumed only the spill-

179 over rate is time-dependent and the flexibility is determined by BIC.

180 Results

181 Figure 2 shows the spatio-temporal patterns of MERS-CoV overall human cases in Saudi

182 Arabia and worldwide, monthly percentages of MERS-CoV infectious camels in Saudi Arabia

183 [24], noting Hajj and Ramadan periods. The top panel shows the distribution of confirmed

184 cases of MERS-CoV infection worldwide, which are mostly concentrated in the Middle East,

185 followed by the Republic of Korea, and have spread to 27 countries. The bottom panel shows

186 the temporal patterns of MERS-CoV human cases and percentages of MERS-CoV camels

187 cases. Major MERS-CoV waves peaked in May 2014, February 2015, June 2015 (South

188 Korea), August 2015 and March 2016. Most of them occurred mainly in Saudi Arabia, except

189 that the third wave occurred mainly in the Republic of Korea. The percentage of MERS-CoV

190 infectious camels showed three waves in a year (May 2014 to April 2015) which were followed

191 by three waves in the weekly human MERS-CoV confirmations. This phenomenon suggests

192 that the waves in the human cases could be driven by the epidemic waves of infections among

193 camels.

194 The transmission rate, β, can be affected by climatic factors, as well as closing-and-

195 reopening of markets during general holidays or religious festivals. Thus, we used a cubic 196 spline to model the transmission rate. We uniformly distributed nβ nodes over the time 197 period, where nβ is to be estimated. The cubic spline function was a smooth function that 198 passed through the nβ nodes. We compared models with different number of nodes and found 199 the best model which attained the smallest BIC. We fixed the following parameters within

200 biologically reasonable ranges: the lifespan of camels at 14 to 20 years, the latent period at

201 2 days, and the infectious period at 4 days. The results are shown in Figure 3. Panel (a) −1 202 shows the case of the life span µ of 14 years, while panel (b) shows that of 20 years. The

6 80

60

● ●● ●●● ● ● ● ● 40 ● ● ● ● ● ● ●●● ● ● ●●●● ●●● ● ●● ●●●● ● ●●●●●●●●● ● ●●● ●●● ●●●●● ●● ● ●●●●● 20 ●●●● ●●● ● ●

● ● 0

Saudi Arabia 1303 −20 Republic of Korea 185 United Arab Emirates 72 Jordan 27

−40 Qatar 19 other 56

● Confirmed −60

−150 −100 −50 0 50 100 150 ●● 100 Percentage of MERS−CoV camels 30 ● ● 25 MERS−CoV worldwide 20 MERS−CoV in Saudi Arabia 15 80 10 ● 5 0 % MERS Camels

60 ● ●

Hajj Hajj Hajj Hajj ● Hajj Hajj 40 ●● Ramadan Ramadan Ramadan Ramadan Ramadan ● ● ● ● ● ● ● ● ● 20 ●● ● ● ● ● Weekly MERS−CoV Confirmations Weekly ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ●●● ●●●● ● ● ● ●●● ● ● ●● ● ● ● ● ● ●●●● ● ● ●● ●●● ● ●●● ● ● ● ● ●● ● ●● ● ●● ● ●● ● ● ● ● ● ● ●● ●●●● ●● ● ● ● ●●●●● ●●●● ● ●●●● ● ●●●● ● ●● ●●● ● ● ●●●● ● ●●●●●● ●●●●●●●●●●● 0 ●●●●●● ●●●●●●●●●●●●●● ●●●●●● ● ●● ●●● ●●●●● ●●●

Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep 2013 2014 2015 2016

Figure 2: Spatio-temporal patterns of MERS-CoV human cases and percentage of MERS- CoV camels. The top panel summarises the cumulative global cases from September 2012 to May 2016. The bottom panel shows the weekly confirmed cases of MERS-CoV human cases worldwide (red lines with circles) and in Saudi Arabia only (black lines with diamonds). Bold black curve shows monthly percentage of MERS-CoV infectious camels during May 2014 to April 2015. There were three waves in the MERS-CoV camels which were followed by three waves in the weekly human MERS-CoV cases. We also showed the period of religious events, Hajj (light grey vertical dash line) and Ramadan (shaded bars). The map was made with R programming language, and the country borders were downloaded from Sandvik B., World Borders Dataset, http://thematicmapping.org(2009).

203 inset panels on the left show the profile of the model BIC as a function of nβ. In both cases, 204 the smallest BIC was attained when nβ is 10. Therefore, in the main panels, we display the 205 model fitting results with nβ is 10. The inset panels on the right show the profile of MLL as 206 a function of the spill-over rate ρ. In both simulations, the models were able to capture the

207 four major epidemic waves out of six waves during the period. We found that the duration

7 208 of immunity is about one year in both cases, or more specifically, 0.86 year in panel (a) and

209 1.14 year in panel (b). We found that the spill-over rate was about 0.00053 (95% confidence

210 interval (CI) 0.00042, 0.0028) and 0.00065 (95% CI 0.00044, 0.00268), respectively, which

211 corresponded to the prevalence of MERS-CoV infection among camels to be as high as 9%.

212 This largely matched the observed prevalence of 11% [24]. A smaller spill-over rate implies −1 213 a higher prevalence. Through computing the models’ profile MLL as a function of λ , we

214 estimated the 95% CI of the duration of immunity to be (0.34 year, 5.82 years) in panel (a) camels 215 and (0.35 year, 7.09 years) in panel (b). The estimated mean R0 were 2.71 and 3.34.

( a ) ( b ) 8 ● ● ● ● ● ● ● ● ● 12 ● ● ● ● ● ● ● ● ● ● ● 514 ● ● 514 ● ● −225 ● ● −225 ● ● 510 510 ● ● ● ● ●

BIC ● BIC −235 506 MLL −235 506 MLL ● ● ● ● ● ● ● ● ● ● ● ● 10 ● ● −245● ● 502 ● −245● ● 502 ● ● ● 6 6 8 10 12 14 6 8 10 12 14 1e−042e−044e−048e−040.00160.0032 1e−042e−044e−048e−040.00160.0032 nβ ρ nβ ρ

n 8 o

i −1 −1 t µ = 14 years µ = 20 years a σ−1 = σ−1 =

2 days 2 days ) m

− − t

r 1 1 i γ = 4 days γ = 4 days ( f reported cases s −1 −1 l n λ = 0.86 years λ = 1.14 years e o

4 simulation median 6 m c a

= ● = nβ 10 nβ 10 c transmission rate 0 y l R k ●●● ● ● ● e ● ● ●

e ● ● ● ● ● w ● ● ● ●●●●●●●●● ●● ●● ●● ●●● 4 ● ● ● ●● ● ● ● ●●● ● ● ● ● ●● ● ● ●● ● ● ● ● ●● ● ● ●● ● ● ● ●●●●● ● ● ● ●● ●● ● ●● ● ●●●●●●●●● ● ●● ●● ● ● ● ●● ●●● ● ●● ●● ●● ● ●● ● ●●● ●●●● ●●● ●●● ● ● ● ● ●●● ●● ● ● ●●● ● ●● 2 ● ● ● ●●● ● ● ●● ●● ● ● ● ● ●●●●●●●● ● ●● ●● ● ●● ●● ● ●● ● ● ● ●● ●● ●● ● ● ●●●●●● ●●●●●●● ●● ● ● ●● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● 2 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●

0 0 Jan May Sep Jan May Sep Jan May Jan May Sep Jan May Sep Jan May 2014 2015 2016 2014 2015 2016

Figure 3: Model simulations versus observed MERS-CoV spill-over cases. Thin black curve represents reported spill-over cases, bold red curve represents model generated median of 1000 simulations, shaded regions represent the 95% range of simulations, and blue curve (with circles) represents the transmission rate (in units of R0). Inset panels on the left show the profile of BIC as a function of the number of nodes in the transmission rate. Inset panels on the right show the profile of MLL as a function of the spill-over rate ρ, while fixing nβ = 10.

216 The above results used standard model selection approaches to achieve the optimal

217 flexibility in the transmission rate. Recall that the transmission rate could be affected by

218 climatic factors and camels-related activities, thus the real flexibility in the transmission rate 219 could be higher than our model estimate. If we choose a large nβ, such as 17 or 19, we could 220 achieve improved fitting as shown in Figure 4. Panel (a) shows the fitting results with nβ = 17 221 and panel (b) shows that of nβ = 19. In the inset panel, we show the model’s profile MLL as −1 −1 222 a function of λ . The MLL estimates of λ are 0.62 year (95% CI: 0.27 year, 3.07 years)

223 and 0.44 year (95% CI: 0.08 year, 3.23 years). Again, we found that the duration of immunity

224 protection was short. More importantly, the estimated maximum prevalence of MERS-CoV

225 among camels was about 15% which is consistent with a previous study [24]. The estimated

226 spill-over rates were about 0.00039 and 0.00033 respectively, which were lower than those in camels 227 Figure 3. The estimated mean R0 were 3.31 and 2.71.

8 ( a ) ( b ) 8 ● ● ● 12 ● ● ● −211 ● ● ● − −212 ● − ● ● ● ● µ 1 = 14 years ● µ 1 = 14 years ● ● − ● − ● σ 1 = 2 days −214 ● σ 1 = 2 days − ● − −213 ● γ 1 = ● γ 1 = 4 days MLL −216 ● 4 days MLL ● −1 ● −1 λ = 0.62 years ● λ = 0.44 years ● 10 −218 −215 ρ = 0.00039 ● ρ = 0.00033 ●

s 6 nβ = 17 0.1 0.5 2.0 5.0 nβ = 19 0.1 0.5 2.0 5.0 e

s λ−1 λ−1

a ● ● reported cases ● c

● 8 ●

n simulation median ● a ● transmission rate ● ● m ) t u ● ● ( ● h s l ●

● ● e y ● r

4 6 m a a c

● 0 ● ● ● ● ● ● m ●

i ● R

r ● ● ●

p ● ● ● ●● ● ● ● ● ●

y ●

l ● ● ● ● ● k ● ● ● ● ● 4

e ● ● ● ● ●● ● ● ● ● ● e ● ● ● ● ● ● ● ●●●●●●● ● ● ● ● ● ● ●● ● ● ● ● ● w ● ● ●●● ● ● ● ● ● ● ●● ● ● ● ● ● ●●●● ● ● ● ● 2 ● ● ● ● ●●● ●● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ●●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●●●●● ●● ● ● ●● ● ● ● ● ● ● ● ●● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 2 ● ● ●●●●●●● ● ● ●● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●●●●● ●●●●●

0 0 Jan May Sep Jan May Sep Jan May Jan May Sep Jan May Sep Jan May 2014 2015 2016 2014 2015 2016

Figure 4: Model simulations versus observed MERS-CoV spill-over cases. Thin black curve represents reported spill-over cases, bold red curve represents model generated median of 1000 simulations, shaded regions represent the 95% range of simulations, and blue curve (with circles) represents the transmission rate (in units of R0). Inset panels show the profile of maximum log likelihood as a function of the duration of immunity protection.

228 So far, we have limited knowledge about the spill-over rate ρ, and we have assumed it

229 to be constant. It was possible that both transmission rate and spill-over rate could vary

230 over time. However, if we assume both to be flexible and then modelled them as cubic spline

231 functions, the model would be too complex. Alternatively, we could assume the transmission

232 rate to be constant and then allowed the spill-over rate to vary. We repeated the fitting in

233 Figure 3, but assumed constant β and time-varying ρ. We showed the results in Figure 5. −1 234 The BIC is worsened by 4.13, and the difference is marginally significant. The estimated λ

235 is still short, and the results were consistent. The prevalence of MERS-CoV among camels

236 is now lower than 0.04. Thus we rejected this scenario. In reality, the observed patterns in

237 the spill-over cases could be due to variations of other factors. the estimated spill-over rate

238 was about 0.00053 and 0.00056 respectively, which were comparable to that in Figure 3. The camels 239 estimated R0 were 3.67 and 3.88 respectively.

240 Discussion and Conclusions

241 We used a mechanistic model and likelihood-based inference framework to investigate the

242 transmission pattern of MERS-CoV among dromedary camels in Saudi Arabia from January

243 1, 2014 to May 31, 2016. To our knowledge, our methodology in studying MERS-CoV is

244 novel. Previous mathematical modelling studies on MERS-CoV had primarily focused on

245 human-to-human transmission [5, 7, 8, 9, 10, 11, 12]. Our work was largely motivated by the

9 ( a ) ( b ) 8 ● ● 0.0030 µ−1 = µ−1 = 535 14 years 530 ● ● 20 years ● ● σ−1 = σ−1 = 2 days ● 2 days 525 ● −1 ● ● −1 ● γ = 4 days BIC 520 γ = 4 days BIC −1 ● −1 515 ● ● λ = 0.78 years ● λ = 0.83 years 510 ● ● ● 0.0025 camels = ● ● camels = 505 ● ● R 0 3.75 R 0 3.98 s 6 nβ = 8 6 8 10 12 14 nβ = 8 6 8 10 12 14 e

s nρ nρ a reported cases c

0.0020

n simulation median a spill−over rate m u h

) t y ( r 4 0.0015 ρ a m i r p

y l

k 0.0010 e e

w 2

0.0005

0 0.0000 Jan May Sep Jan May Sep Jan May Jan May Sep Jan May Sep Jan May 2014 2015 2016 2014 2015 2016

Figure 5: Model simulations versus observed MERS-CoV spill-over cases. Thin black curve represents reported spill-over cases, bold red curve represents model generated median of 1000 simulations, shaded regions represent the 95% range of simulations, and dashed blue curve represents the spill-over rate. Inset panels show the profile of BIC as a function of the number of nodes in the spill-over rate.

246 serological findings in Sabir et al. [24] which showed that there were high and fluctuating

247 prevalence of MERS-CoV among camels. We noted that the fluctuation of the MERS-CoV

248 camels matched the waves in the weekly human confirmation, although this comparison was

249 done for only one year (May 2014 to April 2015) [24]. For the best-fitting model, the changes

250 in transmission rate compared to the other models were not very dramatic. We considered

251 three modelling scenarios. We found short immunity duration or high replenishment rate of

252 camels. This is in-line with previous serologically studies. For instance, Meyer et al. found

253 that serum from 6 of 11 calves had completely lost their neutralizing activity after 56 months

254 [35]. We also found high prevalence of MERS-CoV infections among camels which matches the camels 255 results from previous virological studies. Finally, R0 ≈ 3 or 4 is biologically reasonable 256 and in-line with that of Severe Acute Respiratory Syndrome (SARS), which also belonged to

257 the same virus family as MERS-CoV.

258 Many external factors could impact the transmission of MERS-CoV among camels, from

259 camels to human, and among humans. The transmission rate of MERS-CoV could vary over

260 time, so did the spill-over rate from camels to human, and transmission rate among human. In

261 this work, we attempt to address the transmission of MERS-CoV among camels and also from

262 camels to human (spill-over). In the future, we could include human-to-human transmission

263 into our framework. The reason we did not include this part in current work is due to lack 264 of detailed data. Since the R0 among human is substantially less than 1, the transmission 265 among human was limited in hospital setting and in household transmission, we believe that

266 the transmission among camels played the key role to form the observed temporal pattern in

10 Table 1: Summary of parameter settings and estimates in Figs 3-5. The mean basic repro- ductive number is defined as R0 = hβi /γ, where h·i is the time average. S.0, E.0, I.0, and R.0 are initial conditions; In Figs 3 and 4, ρ is assumed constant and β(t) is time-dependent, whereas these are reverse in Fig 5. Camel population size N=270,000. σ−1 = 2 days. γ−1 = 4 days.

Parameter Fig.3a Fig.3b Fig.4a Fig.4b Fig.5a Fig.5b µ−1 (years) 14 20 14 14 14 20 λ−1 (years) 0.86 1.14 0.62 0.44 0.78 0.83 nβ 10 10 17 19 8 8 hβi 247.01 305.05 301.95 247.65 342.55 363.63 camels R0 2.707 3.343 3.309 2.714 3.754 3.985 hρi 0.000531 0.000653 0.000387 0.000331 0.000542 0.000576 τ 0.003375 0.003784 0.002881 0.004018 0.007507 0.007338 S.0 0.79508 0.593464 0.971608 0.980595 0.196026 0.184083 E.0 0.003552 0.002307 0.001719 0.001047 0.000521 0.000499 I.0 0.003552 0.002307 0.001719 0.001047 0.000521 0.000499 R.0 0.197815 0.401921 0.024954 0.017312 0.802933 0.814919 MLL -219.18 -219.1 -211.49 -210.89 -226.06 -225.89 BIC 501.03 500.86 514.57 523 505.14 504.81

267 human cases.

268 In the main text, we assume that the infection from reservoir was 1/4 due that this

269 number was used in WHO reports [34]. In the Supplementary Materials S2, we show the

270 results when this ratio is 12% [12]. Our main conclusions largely hold. In particular, we

271 observed high rate of loss-of-immunity (and replenishment of susceptible pools), low spill- camels 272 over rate (ie, high prevalence among camels) and reasonable R0 . 273 We proposed a one-host (camel) model in the main text. In the Supplementary Ma-

274 terials, we extended it into a two-host (i.e. camels and human) model and presented some

275 preliminary findings. These results have led to similar conclusions as in a crude one-host

276 model. We considered possible impact of climatic factors (air temperature and absolute hu-

277 midity) and showed preliminary analyses in the Supplementary Materials. There were no

278 evident correlation between MERS-CoV outbreaks and the timing of Hajj.

279 We compared the monthly prevalence of MERS-CoV infections among camels with

280 weekly human cases for a year in Figure 1. The waves in camels cases were followed by the

281 waves in human, which implies that camel cases have led to human cases. Longer surveillance

282 among camels and phylogenetic work are needed to further clarify this issue. Nevertheless,

283 our results will motivate modelling work on the transmission of MERS-CoV among camels.

284 In the Supplementary Materials, we illustrated how a simple two-host model could be re-

285 alized. Our modelling work could be improved if data on primary and secondary human

286 cases are available. Our framework could be extended to incorporate two time series. We

287 assumed constant camels population size, which could be varying indeed. We expected that

288 our fitting could still be robust if the population size changed mildly during a year or over

11 289 the study period. The changes in the population size in a susceptible pool can be translated

290 into changes in the transmission rate [46]. It is challenging but worth trying to model the

291 estimated transmission rate using actual factors such as climate, closing and reopening of

292 markets, holidays or evolution of the virus and come up a mechanistic model of these driving

293 forces.

294 The major strengths of our study are that we had used a simple epidemic model to

295 study the prevalence of MERS-CoV among camels, and that our estimates are biologically

296 reasonable. However, our study was still subject to limitations. First, since current animal

297 health surveillance did not routinely report MERS-CoV cases among dromedary camels, we

298 could only assume that primary human cases were at a ratio to camel cases (i.e. constant or

299 time-varying spill-over rate). These assumptions were appropriate when cases were predomi-

300 nantly zoonotic and that the propensity for MERS-CoV to cross species boundaries did not

301 change over time. In the future, more detailed epidemiological information on human cases

302 could improve the accuracy of estimating weekly primary cases. Animal surveillance and

303 control of MERS-CoV in Saudi Arabia should also target dromedary camels. This could help

304 reduce sporadic introductions to humans. Effective measures to identify, diagnose and isolate

305 infected dromedary camels were much needed. Preventive measures should be undertaken at

306 the animal/human interface to reduce zoonotic transmission of MERS-CoV.

307 Acknowledgement

308 We thank three reviewers for their comments which helped to improve the manuscript

309 substantially. We thank Dr Xin Guo and Mr. C.T. Lo for their technical assistance in

310 helping us to perform our computations on the workstations at the Department of Applied

311 Mathematics of the Hong Kong Polytechnic University.

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15 Supplementary Materials

433 Contents

434 S1 Partially Observed Markov Process 17

435 S2 Assuming Smaller Proportion of Infections Reservoir 17

436 S3 Extension to a Two-Host Model 20

437 S4 Climatic Factors 20

16 438 S1 Partially Observed Markov Process

439 Partially Observed Markov Process (POMP) is a commonly used statistical model that

440 contains two states: ‘hidden states’, which are modeled as Markov process, and ‘observed

441 states’. Figure S1 shows the flow diagram of POMP.

Figure S1: Flow Diagram of Partially Observed Markov Process.

442 In applying POMP, hidden states, X = {X0,X1, ··· ,XT }, are considered as the actual 443 number of camel infections and observed states, Y = {Y0,Y1, ··· ,YT }, are considered as the 444 reported number of human cases. Based on the model structure and these considerations,

445 recursive filtering problem and maximum likelihood estimators are solved by the iterated fil-

446 tering method [40] within a plug-and-play framework [37]. The steps are outlined as follows:

447 i) a fixed time-step Euler-multinomial process is applied to develop a stochastic simulation

448 model, ii) the measurement noise is generated by a negative binomial process, iii) the like-

449 lihood estimation is calculated by particle filtering [47] and Maximum Likelihood Estimates

450 (MLEs) are computed by iterated filtering method, and iv) AICc or BIC is used to evalu-

451 ate performance and to select the best fitting model. Our plug-and-play framework is built

452 on iterated filtering. Compared to other non-plug-and-play methods, such as Expectation-

453 Maximization (EM) algorithm and Markov chain Monte Carlo (MCMC), the iterated filtering

454 overcame the theoretical convergence problems faced by EM and MCMC methods for non-

455 linear POMP models [48]. The implementation is achieved by ‘pomp’ package available in

456 the statistical software R (http://kingaa.github.io/pomp/).

457 S2 Assuming Smaller Proportion of Infections Reser-

458 voir

459 In the main text, we assumed the proportion of infections from camel reservoir is 25%,

460 here we changed this ratio to 12%.

17 ( a ) ( b ) 8 ● ● 12 − ● − ● µ 1 = 14 years ● µ 1 = 20 years ● − 470 − 470 σ 1 = ● σ 1 = ● 2 days ● 2 days ● −1 ● −1 ● γ = 4 days BIC 460 ● γ = 4 days BIC 460 ● −1 ● −1 ● λ = 0.86 years ● λ = 0.81 years ● 10 ● ● ● ● ● ● nβ = 6 450 nβ = 6 450 6 6 8 10 12 14 6 8 10 12 14 nβ nβ

n 8 o i t a ) m t r i ( f reported cases s l n e o

4 simulation median 6 m c a

● c ●●●●transmission●●●●● rate 0 y ●● ●●●

l ● ● ● ●● ● ●● ●●●●●●●●● ● ● ●●● ●●● R k ● ●● ● ●● ●● ● ●● ● ●● ● ●● ● ●● ● ●● e ● ● ●● ● ●● ● ●● ● ●●● ● ●● ● ●● ● ●● e ●● ●● ● ●●● ● ●● ●●● ● ●●● ● ●●● ● ●● ● ● ●●● w ● ● ●●● ● ● ● ● 4 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ●● ●● ●● 2 ●●● ●● ●●●●●● ●●● ●●●●●● ●●●●●● ●●● ●●●●●● ●●● ●●● ●● ●●● ●● ●● ● ●● ●● ● ● ●● ●● ●● ● ● ● ● 2 ● ●● ●● ● ● ●● ●● ● ● ●● ●● ● ● ●● ●● ●● ●● ●●

0 0 Jan May Sep Jan May Sep Jan May Jan May Sep Jan May Sep Jan May 2014 2015 2016 2014 2015 2016

Figure S2: Model simulations versus observed MERS-CoV spill-over cases. Same model input parameters are used as in Figure 3, except that the proportion of infections from camels is 12%.

( a ) ( b ) 8 ● ● ● ● 12 ● ● ● ● ● −1 ● ● −1 ● ● µ = −195.5 ● ● µ = ● ● 14 years ● 14 years −195 ● −1 ● −1 ● σ = 2 days −196.5 ● σ = 2 days ● −1 −1 γ = ● γ = −196 ● 4 days MLL 4 days MLL − −197.5 − ● λ 1 = 0.44 years λ 1 = 0.31 years ● −197 ● 10 ρ = 0.00021 −198.5 ● ρ = 0.00019 ●

s 6 nβ = 17 0.1 0.5 2.0 5.0 nβ = 19 0.1 0.5 2.0 5.0 e

s λ−1 λ−1 a reported cases c

8

n simulation median a ● transmission rate m ) t u ( h s l

e y ●● r ●

4 6 m ● ● a a

● c ● ● 0 ● ● m ● i

● R r ● ● ● p

● ●

y ● ● ● l ●● ● ● ● ● k ● ● ● 4 e ● ● ● ● ● ● ● e ● ● ● ● ● ●●● ●●●● ● ● ● ● ● w ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ●● ●● ●●● 2 ● ●● ●●●● ● ● ●●●● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ●● ●● ● ● ●●●●● ●● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ●● ● ● ●●●● ● ● ● ● ●● ● ● ● ●●●● ●● ● ● ● ●●● ● ● ●● ● ● ● ●● ● ● ●●● ● ●●●●●●●●● ● ● ● ● ●●● ● ● ● ●● ●● ●● ● ●● 2 ● ●● ●●● ●● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ●●●●

0 0 Jan May Sep Jan May Sep Jan May Jan May Sep Jan May Sep Jan May 2014 2015 2016 2014 2015 2016

Figure S3: Model simulations versus observed MERS-CoV spill-over cases. Same model input parameters are used as in Figure 4, except that the proportion of infections from camels is 12%.

18 ( a ) ( b ) 8 ● ● 0.0030 − 480 ● ● ● − 480 ● ● ● µ 1 = 14 years µ 1 = 20 years −1 −1 σ = 2 days 470 ● σ = 2 days 470 ● −1 −1

γ = BIC γ = BIC 4 days ● ● 4 days ● −1 460 −1 460 ● λ = 0.63 years ● λ = 0.48 years ● 0.0025 450 ● ● ● ● camels = ● camels = 450 ● R 0 2.09 R 0 1.87 s 6 nβ = 5 6 8 10 12 14 nβ = 5 6 8 10 12 14 e

s nρ nρ a reported cases c

0.0020

n simulation median a spill−over rate m u h

) t y ( r 4 0.0015 ρ a m i r p

y l

k 0.0010 e e

w 2

0.0005

0 0.0000 Jan May Sep Jan May Sep Jan May Jan May Sep Jan May Sep Jan May 2014 2015 2016 2014 2015 2016

Figure S4: Model simulations versus observed MERS-CoV spill-over cases. Same model input parameters are used as in Figure 5, except that the proportion of infections from camels is 12%.

Table S1: Summary of parameter settings and estimates in Figure S2-S4. Same model input parameters are used as in Table 1, except that the proportion of infections from camels is 12%.

Parameter Fig.S2a Fig.S2b Fig.S3a Fig.S3b Fig.S4a Fig.S4b µ−1 (years) 14 20 14 14 14 20 λ−1 (years) 0.86 0.81 0.44 0.31 0.63 0.48 nβ 6 6 17 19 5 5 hβi 327.95 315.73 268.27 206.04 191.17 170.27 camels R0 3.594 3.46 2.94 2.258 2.095 1.866 hρi 0.000304 3e-04 0.00021 0.000186 0.000367 0.000315 τ 0.00972 0.017374 0.002918 0.005305 0.00765 0.009408 S.0 0.969639 0.988335 0.987012 0.99179 0.479727 0.554365 E.0 0.002068 0.002033 0.001639 0.000917 0.000529 0.000437 I.0 0.002068 0.002033 0.001639 0.000917 0.000529 0.000437 R.0 0.026225 0.0076 0.009711 0.006376 0.519215 0.444761 MLL -202.7 -202.86 -194.98 -194.25 -204.12 -204.28 BIC 448.78 449.11 481.54 489.73 446.8 447.12

19 461 S3 Extension to a Two-Host Model

462 Besides the model for camels in the main text, we include the following two equations

463 for human ˙ Ih1 = ργI − µhIh1 (6a) ˙ Ih2 = r(Ih1 + Ih2) − µhIh2 (6b)

464 where I denotes number of infectious camels, Ih1 denotes primary human cases, and Ih2 465 denotes secondary human cases, and r denotes the ‘transmission rate’ among human. We

466 assumed the susceptible pool of human is very large and remains constant (thus synthesised

467 in r ). There could be other ways to formulate this model. Alternatively, we could define the −1 468 situation as in a hospital or in households, where the susceptibles are very limited, µh = 7 469 days. Since we know that eventually the proportion of primary cases Ih1 is only 25% (or 12%) ˙ 470 among all human cases. Thus we would expect to achieve at equilibrium (when Ih2 = 0) of e 1 e e 3 e 3 88 471 the second equation, Ih1 = 3 Ih2 (or Ih1 = 22 Ih2). This leads to r = 4 µh (or r = 100 µh). We 472 assumed all Ih1 and Ih2 are reported. 473 Then we fit the whole model to all weekly human cases with the moderate primary case

474 ratio 25% as illiustration. The results are shown in Figure S5. The estimated ρ is 0.0005 −1 −1 475 (95% CI 0.0004, 0.0006) in both cases of µ = 13 years and µ = 20 years. The estimated −1 476 λ is 1.25 year and 1.2 years, respectively.

477 This model could be more useful if we have data for separated time series of primary

478 and secondary human cases.

479 S4 Climatic Factors

480 Wavelet analyses are conducted via R package “WaveletComp” (http://hs-stat.com/ 481 WaveletComp/) for exploring the relationships among weekly MERS-CoV human cases and

482 climatic data for Riyadh Saudi Arabia were obtained from Weather Underground Organization

483 (https://www.wunderground.com).

484 Figures S6 and S7 show the results of wavelet coherency analysis for weekly human

485 MERS-CoV cases versus temperature and absolute humidity from June 13, 2012 to October

486 19, 2016 in Saudi Arabia. Black-dashed line in Figure S6(c) suggests there is a possible

487 association between temperature and MERS-CoV cases, where significant synchronization

488 are shown from mid-2013 to mid-2014 and from mid-2015 to early 2016. Synchrony pattern is

489 less evident in MERS-CoV versus absolute humidity. With one-year wavelet period, absolute

490 humidity leads MERS-CoV human cases for about 3 months.

20 ( a ) ( b ) 14 − ● − ● 12 µ 1 = 14 years ● ● µ 1 = 20 years ● ● − − σ 1 = 2 days −325 ● σ 1 = 2 days −325 ● − − ● γ 1 = 4 days ● ● γ 1 = 4 days ● MLL −335 ● MLL −335 ● 12 −1 −1 ● λ = 1.25 years λ = 1.2 years ● ● ● ● ● ● 10 nβ = 10 −345● ● ● ● ● nβ = 10 −345● ● ● ● 5e−05 2e−04 1e−03 5e−05 2e−04 1e−03 10 ρ ρ ● ● ● ● ● ● ● n ● ● ● ● 8 ● o

i ● ● ● ● t ●

a ● ● ● ●●● ●● ● ● ● ● ● ● ● ) m

● t 8 ● ● ● r ● ● ● ● i ● ● ( f reported cases ● ● ● s

● l

n ● ● ● ● ● ● ● ● e o

simulation median 6 m ● ● ● ● ● ● c ● a ● ● ● ● c

● ● 0 transmission rate ● ● ● ● y

l ● ● ● ● ● 6 ● ● ● R k ● ● ● ● ● ● ●

e ● ● ● ● ● ● ● ● ● ● ● ● e ● ●● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●

w ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 4 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 4 ●●● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ●●● ● ● ●

● ● ● ● 2 2 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 0 0 Jan May Sep Jan May Sep Jan May Jan May Sep Jan May Sep Jan May 2014 2015 2016 2014 2015 2016

Figure S5: Two-host model simulations versus observed MERS-CoV human cases. Thin black curve represents reported spill-over cases, bold red curve represents model generated median of 1000 simulations, shaded regions represent the 95% range of simulations, and blue curve (with circles) represents the transmission rate (in units of R0). Inset panels show the profile −1 3 of MLL as a function of the spill-over rate. µh = 7 days, and r = 4 µh.

21 (a) MERS and Temperature 100 MERS cases 40 ● Temperature

80 ● ●●● ●●Hajj ● ●

● ● ● 35 ●●● ● ● ● ●●● ● ●●●●● ● ● ●●●●● ●● ●●● ●●● ● ●●● ● ● ●●● ●●● ●●● ●● ● ● ● ● ●● ● ● ● ●●● ●●●●●● ● ● ●● ● ● ●● 60 ● ● ● ● ●●● ● ●● ● ● ●● ●●●●● ● ● ●● ●● ● ●●● ● ● ● ● ●● ●● ●● ● ●● ● ● ● ●● ●● 30 ● ●● ● ●● ● ● ● ● ● ●●● ● ●●● ● ● ● ● ● ●●● ● ● 40 ● ●● ●● ● ● ● ● ●● ●●● ●● ● ● ● ● ●●● ● ● ● Temperature

MERS cases ●● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● 25 ● ● ● 20 ● ● ●● ● ●● ●● ● ● 0 20

2013 2014 2015 2016

(b) Wavelet Coherencey Analysis ●●●●●●● ●●●●●●●● ●●●●●●●● ●●●●●●●● ●●●●●●●● 0.9 ●●●●●●●● ●● ●●●●●●●● 1 1 ●●●●●●●● ●●●●●●●● ●●●●●●●● ●●●●●●●● ●●●●●●●● ●●●●●●●● ●●●●●●●● Coherence Levels ●● ●● 0.4 ●● ●●● ●●● ● 0.5 0.5 ●●● ●●●● 0.2 0.25 0.25 0.1 0.125 0.125

wavelet period (year) wavelet 0.0 period (year) wavelet 0.0625 0.0625 ● 0.05 ● 0.0 0.1 1 2 3 4 5 5 10 15

(c) Phase and phase differences: wavelet period = 8−13 (weeks) temp cases phase difference π

π 2

0

− π 2 phase difference angle phase difference

− π

1 2 3 4 5

Figure S6: Wavelet Analysis for MERS-CoV cases and temperature in Saudi Arabia. (a) Time series of weekly reported MERS-CoV cases and weekly average temperature in Saudi Arabia. (b) Left panel is the power spectrum of wavelet coherency analysis for reported MERS-CoV cases and temperature, where red color represents high power and blue for low power; the angle of the arrows indicates the phase and those amidst white line indicates significant phase difference at 5% confidence level; white shades indicates boundary effects. Right panel shows the cross-wavelet average power for different wavelet periods and red dots and blue dots show significance at 5% and 10% levels respectively.(c) Phase and phase difference at wavelet period of 8 to 13 weeks (i.e. 0.15 to 0.25 year); red line and blue line represent temperature and MERS-CoV human cases; black-dashed line indicates the phase difference.

22 (a) MERS and Absolute Humidity 100 MERS cases 30 ● Absolute Humidity 80 Hajj 25 ● ● ● ● ●● ● ● ● ● ●● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 60 ● ● ● ● ● ●● ● ●● ● ●●● ● ● ● 20 ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ●●● ● ●● ● ● ● ● ● ● ●● ●●● ● ● ● ● ● ● ●● ● ●● ●● ●● ●● ● ● ● ● ● ● ● ●● ● ● ● ●● ●● ● ● ● ● ●● ● ● ● ●● ● ● ● 40 ● ● ● ● ●● ● ● ● ●●● ● ● ●● 15 ● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ●● ● ● ● MERS cases ● ● ● ● ●●● ●● ● ●● ● ● ● ● ●● ● ● ● ● ● ●● ●●●● ● ● ● ● ● ● Absolute Humidity ● ●

20 ● ● ● ● ● ● 10 ●● ● ● ● 0 5

2013 2014 2015 2016

(b) Wavelet Coherencey Analysis ●●●●●●● ●●●●●●●● ●●●●●●●● ●●●●●●●● ●●●●●●●● 1.0 ●●●●●●●● ●● ●●●●●●●● 1 1 ●●●●●●●● ●●●●●●●● ●●●●●●●● ●●●●●●●● ●●●●●●●● ●●●●●●●● ●●● Coherence Levels ●●●●●● ●●●●●●●● 0.4 ●●●●●●●● ●●●●●●●● ●●●●●● ●●●● 0.5 0.5 ●●●●●●●● ●●●●●●●● ●●●●●●●● ●●●● ● ●●●● ●●●● 0.2 ●●●● ●●●● ● 0.25 0.25 ●●●● 0.1 0.125 0.125

wavelet period (year) wavelet 0.0 period (year) wavelet 0.0625 0.0625 ● 0.05 ● 0.0 0.1 1 2 3 4 5 2 4 6 8 10 12 14

(c) Phase and phase differences: wavelet period = 1 (year) AH cases phase difference π

π 2

0

− π 2 phase difference angle phase difference

− π

1 2 3 4 5

Figure S7: Wavelet Analysis for MERS-CoV cases and absolute humidity in Saudi Arabia. (a) Time series of weekly reported MERS-CoV cases and weekly average absolute humidiy in Saudi Arabia. (b) Left panel is the power spectrum of wavelet coherency analysis for reported MERS-CoV cases and absolute humidity, where red color represents high power and blue for low power; the angle of the arrows indicates the phase and those amidst white line indicates significant phase difference at 5% confidence level; white shades indicates boundary effects. Right panel shows the cross-wavelet average power for different wavelet periods and red dots and blue dots show significance at 5% and 10% levels respectively.(c) Phase and phase difference at wavelet period of 1 year; red line and blue line represent absolute humidity and MERS-CoV human cases; black-dashed line indicates the phase difference.

23