Lockdowns and reopening in heterogeneous countries for containment SARS-COV-2 COVID19: Case Perú

*For public difusion

Juan Carlos Fabián Janampa Energy Consulting Hanan Group Lima, Perú email: [email protected]

Abstract—This document analyzes and forecasting the effects II. EPIDEMIOLOGIC MODELS of strategies the lockdowns and reopening for control epidemic SARS-COV-2 ( COVID-19) in Perú, with high percentage the A. MODEL Age SEIQRD economics of auto sustain and different socioeconomic levels and Model SEIQRD (Susceptible – Exposed – Infected - precariat investment in public health, with multi-ethnic and multi- Quarantine – Recovered - Death) is a model belongs to the geographic realities, proposal strategies for futures confinements family the SIR models (Susceptible Infected and Removed), the in multi diversity societies. Variety of SEIR models are utilized for approach is similar at [1]. In our case uses too five age groups, coherent and verified data series, development SEIRQD finally for forecasting. We analyze Perú as a whole, so too the Junín eight economic activities, and at home and other locations. The department, a region that has elevational floors between 700 - 4200 formulation for each age (a) group is: masl (meter above sea level). This methodology can be applied for 푑푆푎 퐼푏 analysis and decision making in the future days. = −훽푆푎 ∑ 퐶푎푏 ( ) (1) 푑푡 푁푏 푏 Keywords—Strategy Lockdowns, reopening, Epidemiological 푑퐸 푑푆 models and economics, auto sustained, heterogeneous societies, 푎 푎 = − − 휎퐸푎 (2) pandemic COVID19. 푑푡 푑푡

푑퐼푎 I. INTRODUCTION = 휎퐸 − 훾퐼 − 훿 퐼 − 푋퐼 (3) 푑푡 푎 푎 푎 푎 푎 SARS2-COVD19 was first identified in December 19 in 푑푄 Wuhan City. At six March-20 the first case was reported in Perú. 푎 = 푋퐼 − 훾푄 − 훿 푄 (4) The government in sixteen March-20, decreed a rigid quarantine 푑푡 푎 푎 푎 푎 in all countries, only essential activities continue operating, such 푑푅푎 as banks, activities commercial medicals, agricultural activities, = 훾퐼 + 훾푄 (5) 푑푡 푎 푎 commercial and industrial alimentary. The economic activity of the country was reduced at the 40% level. The lockdown extends 푑푅푎 = 훾퐼 + 훾푄 (6) for a hundred days. The measure of confinement was 푑푡 푎 푎 accompanied by high level of financial and economic resources 푑퐷푎 that bordering 15% of GDP, however the practical impact of = 훿푎퐼푎 + 훿푎푄푎 (7) measures economics was leaking, the economy was contracted 푑푡 in levels while -40% at 70 days the confinement. The population 푁푎 = 푆푎 + 퐸푎 + 퐼푎 + 푄푎 + 푅푎 + 퐷푎 (8) at a percentage of 50%, works in a self-sustained way for day- to-day activities in so-called informal activities. In addition, Where: 훽 is the transmission rate, 훾 is the recovery rate, 휎 is people from the capital migrated to their areas of origin due to the latency rate, 훿푎 is the age dependent death rate and 푋 is the their self-employment jobs. After the seventy days, of quarantine rate. 퐶푎푏 is the element ab of contact matrix, in this confinement around 70% the population in their set was case 5x5. 훽 is the probability the becoming infected from close unconfined because the economic forces overflowed the contact with an infected individual. The contact matrix C is the confinement. Although the government designed a phased mean number of contacts among different age groups in the economic recovery plan ahead of time, the process of adapting population [1]. For this SEIQRD model we have developed Biosafety protocols, voluntary stakeholders, the novelty and software in MATLAB. The sectors are included: Home, Others costs of Biosafety measures slowed the process down. For our (Markeplaces, school, recreation). In the economic activities analysis we use existing epidemiological models type SEIRD as included:1.Extractive(Mining,Agriculture,Fishing)2.Manufactu well as develop SEIQRD models with temporal variations of the rer_Industry.3.Trade. variables to optimize economy and levels of confinement all on 4.Transport_storage_and_communications.5.Services. the matlab -mathworks platform. 6.Informal_Agropecuario.7.Informal_No_Agropecuario. Figure 1 Epidemic maturation for regions as percentage of 8.Informal_Other. time to reach initial saturation B. Model SIR with Logistic Curves Simple phenomenological growth models can be useful for estimating transmission parameters and forecasting epidemic trajectories. However, most existing phenomenological growth models only support single-peak outbreak dynamics, whereas real epidemics often display more complex transmission trajectories. Practical method consists in fit multiple logistics waves to an epidemic data. The function is given by equation [3] and [4]

푛 푁푖 퐶 = ∑푖=1 푁 −훼 (푡−휏 (9) 1+( 푖 −1)푒 푖 푖) The analysis of the curve of cases of infected, according to 퐶푖0 the adjustment of mathematical waves [3] is shown in Figure 2, Where C is the cases of infected accumulate. Other where it is observed that there were three key moments in the parameters are calculated across optimization minimize sum of evolution of the pandemic, the reach of a first peak in May-2020, squares for residual values. the beginning of the opening of economic activities in May-2020 and the beginning practically of the total opening July-2020. C. MODEL SEIR and Calculate Effetive Number Figure 2 Picture of Epidemic in Perú with Logistic wave Reproduction Rt model Model SEIRD (Susceptible Exposed Infected Recovered Death) is utilized for the estimate Reproductive Effective Index (Rt) the formulation is based on [5]. The formulation is based over the two key variables 훽 transmission rate and 훿 death rate:

−휆훽(푡−푡0) 훽(푡) = 훽0 + 푎훽푒 (10)

−휆훿(푡−푡0) 훿(푡) = 훿0 + 푎훿푒 (11)

Where 훽0 훿0 푎훽 푎훿 휆훽 휆훿 ∈ ℜ are parameters calculated minimize error from data series of Infected Cases and death cases. Then Rt is: 퐸 휎 (푡)⁄ 퐼(푡) 푅푡 = (12) 훿(푡)+훾

III. ANALYSIS EPIDEMIC IN PERU The population in Perú is around 32 million. Were 24 regions or departments, the geography is multi-diversity. A. Features of population and measures Biosecurity The evolution the epidemic for regions of Perú shown in The population did not initially comply with the quarantine, Figure 1. The high incidence of infected its started in region and the government allowed essential activities such as Ucayali, Lambayeque and Lima. Other regions such as Junín agricultural food production such as the food and medical Amazonas, Puno the epidemic is beginning. Actually, a July industries to not be confined. The isolation measures are verified 2020 Lima was descending infected levels. The levels primary with the google mobility index shown in Figure 3. However, the and secondary medically attention is slightly decentralized. protective measures such as initial handwash masks were deficient due to the low credibility of the damage of the

COVID19 in people as well as a 30 % of the population of Peru does not have potable water service through the pipe network. Although the isolation was applied by the population, we found from the analysis that only in practical terms, it was executed in 50%, as will be seen later. On the other hand, the Biosecurity measures we estimate had a linear and non-exponential behavior as in other countries, they are only becoming more apparent after three months there are greater awareness, protection measures.

For simulations we have developed software epidemiological called HatunMayu, it has also been used software of community math-works [11] and Universidad e Federal do Rio Grande do Sul Porto Alegre Brazil [5]. However, physical distancing is the biggest problem in As well as other research from the University of Oxford over Transport. mobility in education in Perú. This matrix contact is calibrated with register the curves of infected in model SEIQRD. Figure 3 Index Mobility Google Figure 6 Estimation Contact Matrix for age and economic sectors Perú a) Contact Matrix March-2020

B. Economic Activities The informal economy in Perú contributes 19% of GDP, however, it contributes 53% in employment, this feature determines that a large number of people working in the streets, the network social is long and meshed, informal companies with minimum protection and security criteria, therefor high levels of contact, this fact is effectively b) Contact Matrix June-2020 reproduced in the capital cities of the regions. Improperly regulated self-employment is an endemic problem in Peru as shown in Figure 5

Figure 4 Contribution Informal Sector in the Economy

Figure 5 Evolution Informal Sector in the Economy

D. Lockdown execution As of June 30, three phases of confinement are observed, in the first there is a gradual application, a second phase where execution is permanent up to 68%, and the third phase where the confinement is lifted automatically and gradually with a reduction to the 30%. The start of the confinement reduction began the third week of May, this coincides with the index google mobility. Another notable event is that from the second to the third week of May the infected curve was at a local peak, the opening occurred at the local peak. Here is one of the answers to the question of why Peru was with high incidence in C. Contact Matrix for age that period, despite a rigid quarantine, the answer is that the The matrix contact shows the high mobility in Perú, see quarantine was lifted at its peak. Figure 6. For construction, we use as a source of information [7]. Figure 7 Lockdown execution Figure 10. Accelerated Economic Reactivation

In the event that the lockdown had not been carried out, the results would have been catastrophic, with more than 120 thousand deaths and 1 million active infected, the hospital F. Zoom in region Junín system would not have borne such an impact. The investment in public health in Peru in 2018 is 2.7% of GDP according to CEPAL. One of the lowest in the region. Junín is the department in which the government decided to keep the confinement. Below is the Rt index, for his nine Figure 8. Without Lockdown provinces. Two provinces (Junín 4200 masl y Tarma 3000 masl) have Right around 1.0, while that other two provinces (Huancayo 3200 masl and Yauli 3800 masl) your index Rt are 1.5. The explanation for this index in last provinces is that first is hub city and the last is capital agricultural with relationships social close. All these provinces have agriculture and food production and marketing as their main economic activity, essential activities in trust and they did not stop. Figure 11. Index Rt in Junín department (accompany the name, altitude data)

E. Planning Economic Reactivation The pandemic COVID-19 forces and conditions countries to establish a balance between economy and public health, Below we show two scenarios that arose at the beginning of June (Figure 9 and 10), where it is shown that an accelerated reactivation could duplicate those infected. Until today the projection with slow economy has been fulfilled with respect to the projected. We highlight that the economic reactivation requires health protocols that formal companies classified as bureaucratic and claimed that they were not required from informal sector companies. Figure 9. Slow Economic Reactivation

In Appendix show each evolution of the curves the Rt and infected cases, Such analyzes will allow to establish an ideal calibration of the variables in the past time, to incorporate them in the HatunMayu model to define the confinement strategies. G. Altitude effect The Junin’s department has 9 provinces, of which 7 are above 3000 masl. Of these last the Province Junín and Province Tarma their Rt experience drastic reductions despite the fact that they maintained their agricultural activities during confinement.

Figure 12 Altitude effect (4200 and 3000 masl) Figure 14 Reopening Semi-worst scenario Perú

B. Rational Reopening IV. FORECASTING If the lack of confidence is gradual and people After the calibration process of the contact matrix data, intensify their Biosafety measures, 35% less would be based on the analysis of the curves of infected cases and the expected in the number of deaths compared to the Google mobility index, we proceed to make forecasts for Peru worst case scenario. and the department of Junín. A. Opening in Perú Scenario Suboptimals Figure 15 Optimal Reopening Perú If the confinement is lifted without restrictions and people return to the new normality only with mask protection, the result would be a deterioration in the control of the pandemic, the worsening of the situation would be to wait for another spike in infections 20% higher than the existing one.

Figure 13 Reopening Worst Escenario Perú

C. Forecast for Junín We had detected that the provinces of JUNIN have different Rt, in what they are in descending (Provinces of Junín and Tarma), confinement should be made more flexible, in which they are high, it should emphasize economic and physical disconnection and exercise physical distancing, because in the practice is not exercised by people, although they have masks and wash their hands, people walk without physical distance. In If confinement is lifted on June 30, however, people this document we emphasize the forecast for Huancayo, which improve their Biosafety levels another outbreak would be is the capital province of the Junín department, because it is the expected in late July. main province and with a population of more than 0.5 million. a) Suboptimal Lockdowns for Huancayo Province. Confinement, as in Perú, was not initially fully implemented, after four weeks it had recently reached levels close to 70%, however, the population had oscillating behaviors and with a trend towards 30% lack of confinement from the first week of may. Therefore, a confinement similar to that executed will not be profitable because the number of deceased will reach 1,000 by the end of September. essential in heterogeneous countries with a weak health system, Figure 16 Continued Lockdown similar to that executed in the case of Perú more than 100 thousand deaths were avoided. An optimal containment strategy should focus on: • Intensity of virus containment and elimination measures • Regionalize group of provinces, including socioeconomic dynamic interaction between their particular localities in each region • There are hub cities where the strategy should be to decongest, through operational alternations of access roads example central highway and Province Yauli (Oroya)

• The economic disconnection that accompanies the social b) Other Suboptimal Lockdown for Huancayo Province disconnection must be optimized, homogeneous quarantine to a heterogeneous country is suboptimal. If the quarantine was 50% complete all the time until September, the results would not be flattering either, the The heterogeneous behavior of the population has to be number of deaths at the end of September would be 1,100. See managed, a part of the population is ductile to quickly change Figure 17 their social relationship, while a large majority is not aware of Figure 17 50% Lockdown Huancayo province the problem additional there is a pre-Hispanic social relationship of attending market fairs and being sensitive to the close affection of the people for that group they must invest in practical physical distancing. The physical distance in Perú must be exercised, only communications measures are not sufficient. Portable electronic distance devices are required by people with panic alarms when there is closeness between people less than 1 m. A confinement is a governmental administrative decision, but the confinement is a choice of the population, the balance, health and economy is executed automatically if it was not designed optimally the economic forces are in charge of the

balance. In heterogeneous countries, it is more difficult c) Optimals Lockdowns for Huancayo Province. managing control of a pandemic is complex and requires The optimal planning of Lockdown is maintaining execution difficult decisions levels of 80% in July and August , and 50% in September, the There is a relationship between the altitude and the results are numbered deaths around 700, can be they could even transmission of the disease, the provinces of the department of be minor if people exercise physical distancing. Junín have between 0.1% to 0.25% of the cases of infected with respect to their population, well below the national average of Figure 18 Optimal Lockdown Huancayo Province 1%. Likewise, the evolution of the Rt is consistently descending in the province of Junín at more than 4,200 masl and Tarma at 3200 masl, currently the Rt is less than 1, despite not stopping its activities fully. A methodology is shown that could be replicated to any geographical area of Perú, and of any region that have a high relationship of physical-economic connectivity.

ACKNOWLEDGMENT Acknowledgment to my parents, my teachers and my family.

REFERENCES

V. CONCLUSSIONS [1] D. Baqaee, E. Farhi, M. Mina and J. Stock, “Reopening Scenarios,” The impact of COVID-19 in heterogeneous countries affects National Bureau of Economic Research, Working Paper 27244.May-2020 more intensely and adversely because the different behaviors of [2] N. Sharma A. Kumar Verma and A. Kumar Gupta Spatial Network based people according to their socioeconomic conditions and model forecasting transmission and control of COVID-19,, Pre-print., government economic measures do not homogeneously reach MedRxiv2020.05.06.20092858 , May 2020. all sectors of the vulnerable population. Lockdown’s are [3] M. Batista “Estimation of the final size of the COVID-19 epidemic”, [7] C. Grijalva, N. Goeyvaerts, H Verastegui, K. Edwards, A. Gil, C. Lanata, University of Ljubljana, Slovenia MedRxiv2020.02.16.20023606 Feb- N. Hens, “A Household-Based Study of Contact Networks Relevant for 2020. the Spread of Infectious Diseases in the Highlands of Peru,” PLOS ONE [4] C. Y. Shen, “Logistic growth modelling of COVID-19 proliferation in |DOI:10.1371/journal.pone.0118457 March - 2015. China and its international implications,” International Journal of [8] INEI - National Institute of Statistics and Informatics “Production and Infectious Diseases 96 (2020) pages 582 589. employment informal in Perú Satellite Account of the Informal Economy [5] P. Zingano, J. Zingano, A Silva, C. Zingano, “Defining and computing 2007-2018”. Nov-2019. reproduction numbers to monitor the outbreak of Covid-19 or other [9] Health Ministery Perú reports COVID-19. epidemics,” doi:10.20944/preprints202006.0370.v1 June-2020. [10] Institue Epidemiological Perú reports COVID-19. [6] V. Emanuele, L. Vannucci, “Forecast Covid-19 end date in Italy by [11] CEPAL. Social Panorama report 2019. logistics waves,” Pisa University and Florence University Pre-print May- Software:https://la.mathworks.com/matlabcentral/fileexchange/76956- 2020 publish for discussion. fitvirusxx

APPENDIX Number Reproductive Rt Junín Department

COVID Evolution in each provinces of Junín Department