Modelling Immunization Strategies with Cytomegalovirus Vaccine Candidates
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Epidemiol. Infect. (2011), 139, 1818–1826. f Cambridge University Press 2011 doi:10.1017/S0950268811000343 Modelling immunization strategies with cytomegalovirus vaccine candidates R.S. AZEVEDO1* AND M. AMAKU2 1 Departamento de Patologia & LIM 01 HC, Faculdade de Medicina, Universidade de Sa˜o Paulo, Brazil 2 Departamento de Medicina Veterina´ria Preventiva e Sau´de Animal, Faculdade de Medicina Veterina´ria e Zootecnia, Universidade de Sa˜o Paulo, Brazil (Accepted 16 February 2011; first published online 14 March 2011) SUMMARY In order to analyse the impact of vaccination against cytomegalovirus (CMV) on congenital infection incidence using current vaccines tested in phase II clinical trials, we simulated different scenarios by mathematical modelling, departing from the current vaccine characteristics, varying age at vaccination, immunity waning, vaccine efficacy and mixing patterns. Our results indicated that the optimal age for a single vaccination interval is from 2 to 6 months if there is no immunity waning. Congenital infection may increase if vaccine-induced immunity wanes before 20 years. Congenital disease should increase further when the mixing pattern includes transmission among children with a short duration of protection vaccine. Thus, the best vaccination strategy is a combined schedule: before age 1 year plus a second dose at 10–11 years. For CMV vaccines with low efficacy, such as the current ones, universal vaccination against CMV should be considered for infants and teenagers. Key words: Cytomegalovirus vaccine, immunity waning, immunization strategies, modelling. INTRODUCTION adolescence, when seroprevalence increases again [1, 2]. These observations suggest that the force of Cytomegalovirus (CMV) infection may be the cause of infection, defined as the per capita rate at which mental retardation and deafness in newborns, infec- susceptible individuals acquire infection, may be re- tious mononucleosis syndrome in young adults, and presented by a bimodal pattern. The increase in sero- also pose a threat for immunosupressed individuals. prevalence in teenagers may be related to sexual CMV becomes latent after primary infection. activity [3]. Immunization strategies should consider CMV infection presents distinct phases of trans- infants and teenagers whenever CMV vaccine is first mission with a different age-dependence from other introduced in a population. directly transmitted viral diseases. Seroprevalence An average of 1% of all infants are infected with data from high-incidence CMV communities revealed CMV in utero, and it appears that more infants were that CMV infection occurs initially during the first damaged by CMV infection than by infections such as 3 years of life, stabilizing until the beginning of rubella or Haemophilus influenzae type b meningitis before vaccination reduced the incidence of these in- * Author for correspondence: Professor R. S. Azevedo, fections [4]. Departamento de Patologia, Avenida Doutor Arnaldo 455, Sa˜ o It has long been demonstrated that routine im- Paulo, SP, 01246-903, Brazil. (Email: [email protected]) munization of healthy women aged 15–25 years is Downloaded from https://www.cambridge.org/core. IP address: 170.106.35.234, on 01 Oct 2021 at 13:26:50, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0950268811000343 Modelling cytomegalovirus immunization 1819 cost-effective even in populations with CMV sero- prevalence as high as 87% [5], but at present there is ω no available CMV vaccine. It is, however, likely that a svφ vaccine will be available in the near future [6] and s0 therefore optimal immunization strategies should be λ considered based on the population dynamics of CMV. Griffiths et al. [7] have modelled CMV population h dynamics and control by vaccination assuming life- δ long immunity and a constant force of infection, i0 which is a limitation when considering optimal strat- γ egies for vaccine introduction into a population. il The aim of this study is to develop a mathematical ρ model for CMV dynamics in order to evaluate the impact of vaccination in congenital cases and infec- tion in individuals, estimating an age-dependent Fig. 1. Compartmental model showing the proportion of force of infection from seroprevalence data using individuals in relation to CMV infection status, namely: s, mathematical modelling, and analysing the effects of susceptible; h, harbouring and incubating CMV; i, infec- tious; l, latent and v, vaccinated individuals. The transition different scenarios: varying age of vaccination, im- rates in compartments are indicated (Greek letters; see text munity waning, vaccine efficacy and mixing patterns. for details). The proportions of newborns susceptible (s0) and infected (i0) are also indicated. METHODS Serological data waning), r is the rate latent individuals reactivate CMV infection. Values for constant rates like d, c, w Serological data from Sa˜ o Paulo, Brazil, were used do and r are not well known. The evidence available in determine the age-dependent seroprevalence (0–40 the literature is related to severe cases and is not rep- years age group) [1]. resentative of the average infection. There is some controversy regarding the time to recover from CMV Mathematical model infection. Therefore two different values for c were used in the simulations (Table 1). The Appendix The model proposed has five state variables depen- shows how the system of equation (1) is derived from dent on age a: proportion susceptible, s(a); harbour- the number of individuals in each compartment. ing and incubating CMV, h(a); infectious, i(a); latent, The force of infection l(a), defined as the per capita l(a); and vaccinated, v(a) individuals (Fig. 1), solved rate at which susceptible individuals acquire infection, by the following differential equations: is given by [8]: 9 ds(a) > Z O =(xl(a)s(a)xv(a)s(a)+wv(a)) > > l(a) b(a, a0)i(a0)da0, (2) da > = h a > 0 d ( ) > =(l(a)s(a)xdh(a)) > a a da => where b( , k) is the contact rate for individuals of age di(a) a with individuals of age ak. From seroepidemiological =(dh(a)xci(a)+rl(a)) > (1) da > data published previously [1], it was observed that > dl(a) > seroprevalence increases in two distinct phases sep- =(ci(a)xrl(a)) > da > arated by an almost stable plateau. > dv(a) ;> In order to fit the seroprevalence profile above, the =(v(a)s(a)xwv(a)) da contact rate matrix may be represented by combining where v(a) is the force of vaccination (rate of vacci- age groups in the following manner: children– nation as in [8]), d is the inverse of the incubation children (peak 1), adults–adults (peak 2), children– period, c is the inverse of time to recover from infec- adults (peak 3) and adults–children (peak 4). tion to become latent, w is the inverse of time taken Based on this profile, we selected a composition of to lose the protection given by vaccine (immunity gaussian functions to represent b(a, ak). The resulting Downloaded from https://www.cambridge.org/core. IP address: 170.106.35.234, on 01 Oct 2021 at 13:26:50, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0950268811000343 1820 R. S. Azevedo and M. Amaku Table 1. Notation, biological meaning and values and assumed of the parameters used to simulate scenarios Yv([ai, af]) with the mathematical model i0=0Á01 , (5) Y0([ai, af]) Notation Biological meaning Value where s0 and i0 are the proportions of susceptible 1/w Time to lose vaccine 2 yr, 10 yr, 20 yr, and congenitally infected newborns, respectively, protection no waning s0+i0=1, keeping the population constant, Y0([ai, af]) 1/d Incubation period 2 weeks and Y ([a , a ]) are the proportions of new infections . v i f 1/c Time to recover from 1 5 or 6 months between ages a and a before and after vaccination, infection i f 1/r Time to reactivate CMV 20 years respectively, estimated by [9]: infection Y0([ai, af])=s(ai)xs(af) (6) and Yv([ai, af]) ffi l(af)xl(ai): (7) ad hoc function is the following: The age interval a 10 years to a 40 years corre- ()"# i= f= 2 0 2 sponds to the fertile period when vertical transmission 0 1 axx1 a xx1 b(a, a )=b1 exp x + 2 s1 s1 is likely [10], introducing infected newborns to com- ()"# partment i(a). It is accepted that 1% of newborns 2 0 2 1 axx2 a xx2 are infected in utero by CMV [4]. In our model we +b2 exp x + 2 s2 s2 assumed that with vaccination a decrease in incidence ()"# 2 0 2 of infected newborns will occur, expressed in 1 axx1 a xx2 +b3 exp x + equation (5). 2 s3 s3 ()"# 2 0 2 1 axx2 a xx1 +b4 exp x + Vaccine characteristics assumptions 2 s4 s4 (3) Candidate vaccines under phase 2 trials are live- attenuated or recombinant vaccines [11]. From a where b1, b2, b3 and b4 are parameters related to the theoretical perspective, live-attenuated virus vaccines amplitude; x1 and x2 are the average ages of trans- have the potential capacity to mutate and regain mission for children and adults, respectively; and s1, virulence as they replicate in the vaccinee, as observed s2, s3 and s4 are the standard deviations related to the for poliomyelitis oral vaccine [12]. Another safety width of the function in each peak. issue, when dealing with a herpes virus like CMV, is In the model, we tested three different mixing the fact that such viruses become latent in their hosts, patterns regarding the combination of those peaks: being able to cause disease by reactivation some time pattern I – peaks 1 and 2 (assortative matrix); pattern in the future [13].