key: cord-0943822-6epfkl3g
authors: Honfo, S. H.; Taboe, B. H.; Glele Kakai, R.
title: Modeling COVID-19 dynamics in the sixteen West African countries
date: 2020-09-07
journal: nan
DOI: 10.1101/2020.09.04.20188532
sha: 034fb83ae8e95785ddbd7260e1d195dbbbc5d353
doc_id: 943822
cord_uid: 6epfkl3g

The current COVID-19 pandemic has caused several damages to the world, especially in public health sector. This study considered a simple deterministic SIR (Susceptible- Infectious-Recovered) model to characterize and predict future course of the pandemic in the West African countries. We estimated specific characteristics of the disease's dynamics such as its initial conditions, reproduction numbers, true peak, reported peak with their corresponding times, final epidemic size and time-varying attack ratio. Our findings revealed a relatively low proportion of susceptible individuals in the region and in the different countries (1.2% across West Africa). The detection rate of the disease was also relatively low (0.9% for West Africa as a whole) and < 2% for most countries, except for Cape-Verde (9.5%), Mauritania (5.9%) and Ghana (4.4%). The reproduction number varied between 1.15 (Burkina-Faso) and 4.45 (Niger) and the peak time of the pandemic was between June and July for most countries. Most generally, the reported peak time came a week (7-8 days) after the true peak time. The model predicted 222,100 actual active cases in the region at peak time while the final epidemic size accounted for 0.6% of the West African population (2,526,700 individuals). Results obtained showed that the COVID-19 pandemic has not severely affected West Africa as noticed in other regions of the world, but current control measures and standard operating procedures should be maintained over time to ensure trends observed and even accelerate the declining trend of the pandemic.

Mathematical and statistical models can be extremely helpful tools to make decisions 29 in public health. They are also important to ensure optimal use of resources to reduce 30 the morbidity and mortality associated with epidemics, through estimation and predic-31 tion [27] [28] [29] [30] 33] . The prediction of essential epidemiological parameters such as the peak 32 time, the duration and the final size of the outbreak is crucial and important for pol- 33 icy makers and public health authorities to make appropriate decisions for the control 34 of the pandemic [32] . Therefore, modelling and forecasting the numbers of confirmed 35 and recovered COVID-19 cases play an important role in designing better strategies for 36 the control of the COVID-19's spread in the world [27, 29] . Since the appearance of 37 the first COVID-19 case in the world, several studies have been conducted to model 38 the dynamics of the disease. The main methods used were: deterministic modelling 39 techniques (SIR, eSIR, SEIR, SEIRD, etc. compartmental models) [24, 29, 30, 33, [41] [42] [43] , 40 autoregressive time series models based on two-piece scale mixture normal distribu-41 tions [27] , stochastic modelling methods [49, 50] , machine learning techniques [47, 48] , 42 growth models [43, 52, 53] and bayesian method [48] . 43 Among these modeling techniques, deterministic models are the most considered 44 because of their simplicity. However, they fail to provide accurate results due to non- 45 identifiability problem when the number of compartments and the number of parameters 46 are high [39] . Actually, complex deterministic models have been showed to be less 47 reliable than simpler model such as SIR model framework [39] , which performs better in 48 describing trends in epidemiological data. This under-performance may be worse when 49 meta-population confirmed-cases data are considered. However, only few studies related 50 to COVID-19 in Africa used mathematical models and prevalence data to study the 51 dynamics, analyze the causes and key factors of the outbreak [24, 25, 51] . Recently, [24] 52 assessed the current pattern of COVID-19 spread in West Africa using a deterministic 53 compartmental SEIR-type model. 54 In this study, we used a simple deterministic SIR model to characterize and predict 55 future trend of the spread of the pandemic in West Africa. Specifically, we aimed 56 to estimate specific characteristics of COVID-19 dynamics (initial conditions of the 57 pandemic, reproduction numbers, true peak, reported peak and their times and dates, 58 final epidemic size and time-varying attack ratio). The originality of this work is that it 59 focuses on the sixteen West African countries and the whole region as well. It is the first 60 r 4, 2020 3/24 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted September 7, 2020. . https://doi.org/10.1101/2020.09.04.20188532 doi: medRxiv preprint study dealing with the dynamic of the pandemic in each of the West African countries. 61

Model description 63 Problems of non-identifiability in parameters estimation in deterministic compartment 64 models (especially complex models) are common in epidemiological modelling studies, 65 which often imply biased estimations of parameters. [39] recommended the use of simpler 66 models which overperformed complex models in estimating reliable parameters. Hence, 67 in this study, the simple SIR model [31] was considered with the particularity of two 68 removal rates and illustrated in the system below [17] :

with initial conditions,

In (1), S = S(t), I = I(t) and R = R(t) represent the number of susceptible, infected and 70 removed individuals at time t, respectively while N is defined as the total population size 71

for the disease transmission. The parameters β , ν 1 and ν 2 are the transmission rate, the 72 removal rate of reported infected individuals (detected) and the removal rate of infected 73 individuals due to all other unreported causes (mortality, recovery or other reasons), 74 respectively. We considered the removal rate ν 2 as constant with value ν 2 = 1/10 [54] . 75 From the second differential equation of (1), one can notice that ν 1 I 0 represents the 76 daily confirmed cases (Ir 0 ) at time 0 of the outbreak. Thus, the relationship between 77 the initial number of infected individuals and the detection rate, ν 1 is as follow and used 78 in the estimation process: 79 r 4, 2020 4/24

Data consideration and parameter estimation procedure 81 For each country, the data considered for the modeling spans the period from the date 82 of detection of the first case of COVID-19 in the country and August, 12, 2020. Data 83 considered were the daily numbers of reported cases that have been assimilated to ν 1 I. 84

These data were downloaded from the Global Rise of Education website [55] . Table 1 85 presents the demographic patterns [11] , initial dates of the pandemic [55] and testing 86 efforts (identification of new cases) of the countries [11] . We fitted the model (1) to the 87 observed daily cases to study the dynamics of COVID-19 pandemic in the sixteen West 88

African countries.

To improve the prediction power of (1), we used a cross-validation procedure of 90 used as the measure of estimation precision:

whereθ and θ are the predicted and observed number of daily cases respectively; k 95 is the number of observations considered. We considered as RMSE 1 , the Root Mean 96

Square Error computed on the 90% of the observations and RMSE 2 , computed on the 97 remaining observations (10%)

The solutions of (1) were obtained using the built-in function ODE45 of Matlab [56] . 99

Then, the non linear least square estimate technique was performed to estimate the 100 six parameters in (1) given starting values, using the built-in function fminsearchbnd of 101

Matlab [56] . . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted September 7, 2020. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted September 7, 2020. . https://doi.org/10.1101/2020.09.04.20188532 doi: medRxiv preprint tion, caused by an average infected individual (during his infectious period), in a fully 117 constituted population:

-Running reproductive number, R e [1] : measures the number of secondary infections 119 caused by a single infected individual in the population at time t.

-True peak size, n pp and True peak time, T pp . The true peak size indicates the largest 121 daily number of new infectious cases in the population:

while the true peak time, T pp represents the time at which the largest daily new infected 124 cases is obtained. These two parameters were determined numerically.

-Reported peak size, n rp and Reported peak time, T rp . The reported peak size indicates 126 the largest number of daily reported cases:

while the reported peak time is the associated time to n rp . They were determined 129 numerically.

-Maximum number of active cases, I max : since I 0 , R 0 << S 0 , we assumed the number 131 of initial susceptible individuals to be approximately equal to N (S 0 ≈ N). Thus, I max 132

can be approximated as follow [16] :

-Final epidemic size, I total [16] : it is the total number of cases over the course of the 134 epidemic wave.

S ∞ can be approximated considering the entire population as initially susceptible (S 0 ≈ 136 N); hence, following [16] :

r 4, 2020 7/24 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted September 7, 2020. . https://doi.org/10.1101/2020.09.04.20188532 doi: medRxiv preprint For each country, the equation (7) was solved numerically to determine S ∞ through an 138 iterative process.

-Attack ratio, A r [17] : is the fraction of susceptible population that becomes infected. 140

It is calculated along the epidemic wave as follow: respectively. The proportion of the susceptible individuals across West Africa was also 162 r 4, 2020 8/24

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted September 7, 2020. . https://doi.org/10.1101/2020.09.04.20188532 doi: medRxiv preprint relatively low (1.2%) ( Tables 1 and 2) . Moreover, before the detection of the first cases, 163 infected individuals were present in the population of all the countries with some already 164 recovered individuals. The detection rate of infected individuals was relatively low (less 165 than 1%) for Benin, Burkina, Mali, Niger, Nigeria, Sierra-Leone and West Africa as a 166 whole. However, some countries like Cape-Verde (9.5%) Mauritania (5.9%) and Ghana 167 (4.4%) recorded the highest detection rates, respectively. (Table 3) . 168 In most countries, the model estimated an average of 1 new case of infection caused by 169 an infected individual during his infectious period (R 0 ) except for Sierra-Leone, Nigeria, 170 and Côte d'Ivoire with R 0 ≈ 2 and Niger, which recorded the highest reproduction 171 Table 3) .

Long term dynamics of COVID-19 in West Africa 173 We analyzed the long term dynamic of COVID-19 in West Africa by first focusing on the 174 true peak of the pandemic. In general, the estimated reported peak time came a week 175 (7-8 days) after the true peak time in all the countries while their estimated reported 176 peak sizes accounted in average for 21% of the estimated true peak size (Table 3) Nigeria (5th), Senegal (18th), Guinea (23th) and Cape-Verde (22th) and October 4th 181 for Togo. Niger recorded the earliest true peak time (April 8th) while the latest true 182 peak time was on December 10th, 2020 for Gambia ( Figure 1 and Table 3 ). The true 183 peak time across the region was July 1st with 25,267 new cases (Table 3 and Figure 4a (Table 3 and Figure 1 ). The estimates of the reported peak size was 1,891 daily cases 189 across the region (Table 3 and Figures 4a-b) . . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted September 7, 2020. . Table   2 .

Estimates with 95% confidence intervals of the initial parameters of the SIR-model; . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted September 7, 2020. . Table   3 .

Epidemiological statistics with their 95% confidence intervals indicating the dynamics of COVID-19 in the whole west African region and per country . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted September 7, 2020. . https://doi.org/10.1101/2020.09.04.20188532 doi: medRxiv preprint

The final epidemic size would account for 0.6% of the population of West Africa. 191 This estimate is generally low (< 1% of the population size) for more than half of the 192 countries though Gambia, Guinea-Bissau and Cape-Verde would record the highest final 193 epidemic sizes (> 9% of their populations). The estimates of the maximum number of 194 actual daily active cases at peak time are for most countries greater than 1,000 cases, 195 though, it is 107, 200 and 195, 000 for Niger and Nigeria respectively (Table 3) . . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted September 7, 2020. . https://doi.org/10.1101/2020.09.04.20188532 doi: medRxiv preprint

The running reproduction number helped assess the evolution trend of the disease. 199 It decreased over time in all countries from the beginning of the outbreak (1.2 − 4.5) to a 200 stability point, which varied according to countries (0.50 − 0.82, Figure 2 ). As expected, 201 the fraction of susceptible individuals being infected (attack ratio) increased over time 202 from 0% to 40% − 70%, depending on countries. These evolving trends in reproduction 203 number and attack ratio are similar to those noted for West Africa as a whole (Figure 204 4b-c). . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted September 7, 2020. . . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted September 7, 2020. . https://doi.org/10.1101/2020.09.04.20188532 doi: medRxiv preprint

In epidemiology, understanding the dynamics of an epidemic outbreak and predicting 212 its future course is a major research question, which is often studied using modelling 213 techniques [2, [18] [19] [20] [21] [22] [23] . Estimation and prediction rely on mathematical and statistical 214 models, which inform public health decisions and ensure optimal use of resources to re-215 duce the morbidity and mortality associated with epidemics [14, [27] [28] [29] [30] 33] . For instance, 216 estimation of epidemiological parameters and prediction on the Influenza outbreak dy-217 namics in Canada was done using the Richard's model [14] , while a three-parameter 218 logistic growth model was used to study and forecast the final epidemic size in real-time 219 of the Zika virus outbreaks in Brazil from 2015 to 2016 [2] .

In this study, we used deterministic SIR model to understand COVID-19 dynamics 221 in West African countries and estimated the overall number of susceptible individuals 222 that accounted for 1.2% of West African population and 1% for most countries, except 223

Guinea-Bissau, and Gambia where the susceptible individuals account for more than 224 9%. In general, small countries with relatively high population density are those with 225 high proportion of susceptible individuals, indicating how high population density with 226 small area can affect epidemics dynamics [57, 58] . Our findings however, revealed a 227 great disparity between countries in terms of testing rate of COVID-19. Countries like 228

Guinea and Gambia and in less extent, Côte d'Ivoire and Nigeria, showed a relatively 229 less testing effort to identify many infected individuals. This suggests that there may 230 not be enough tests being carried out to properly monitor the outbreak [55] . In contrast, 231 countries like Cape-Verde, Benin and Togo, which have recorded less than or equal to 50 232 positive cases per 1,000 tests, seem to be effectively controlling the pandemic according 233 to the WHO criteria [45] . Compared to relatively wealthier countries like Australia, 234 South Korea and Uruguay, it takes hundreds of tests to find one case [55] . 235 The detection rate considered in model (1) is a better indicator of testing effort since 236 it represents the proportion of active cases in the population that are identified daily. 237

Our results revealed a relatively low detection rate of COVID-19 in West Africa with less 238 than 2% in most countries except Cape-Verde, Mauritania and Ghana (> 5%). These 239 three countries are also the ones with the highest testing rates (see table 1) confirming 240 the link between detection rate and testing effort [5] . Thus, fairly low detection rates 241 r 4, 2020 15/24 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted September 7, 2020. . https://doi.org/10.1101/2020.09.04.20188532 doi: medRxiv preprint in most West African countries demonstrate low testing effort and may be explained by 242 a number of factors, including the availability of testing kits and qualified healthcare 243 workers and low ability to control the disease due to their low GDP. For instance the 244 average detection rate of COVID-19 in the world in April 2020 was estimated at 6% [59] . 245 It is also useful to note that the estimated average detection rate hides a great variability 246 in the testing effort over time. Indeed, it is generally accepted that the testing rate is 247 relatively low at the very beginning of an epidemic outbreak but can increase rapidly 248 over time when a better response mechanisms are put in place [60] . Our study shows that the novel COVID-19 pandemic, although highly contagious has 269 not seriously impacted West Africa in terms of prevalence, compared to other parts of the 270 world, in particular the Europe and the USA. Actually, the total number of susceptible 271 r 4, 2020 16/24 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted September 7, 2020. . https://doi.org/10.1101/2020.09.04.20188532 doi: medRxiv preprint individuals and final epidemic size account for 1.2% and 0.6% of the total population 272 size of West Africa, respectively. But the relatively low reported cases are related to very 273 low testing effort in the West African countries. The study also indicates a relatively 274 low detection rate and for most countries in the region, the dates of the true peak 275 of infection have passed (June-July 2020). Nevertheless, the pandemic is still ongoing 276 in the region and it is important that the non-pharmaceutical measures currently in 277 place continue over time to help reduce its spread dynamics, pending adequate effective 278 treatment. The authors declares no conflict of interest.

Characteristics of an epidemic outbreak with a large initial infection size

Simple framework for real-time forecast in a data-limited situation: the Zika virus (ZIKV) outbreaks in Brazil from 2015 to 2016 as an example

RRichards model revisited: Validation by and application to infection dynamics

Coronavirus disease 2019 (COVID 19) and Malaria. Have anti glycoprotein antibodies a role

Estimating the true (population) infection rate for COVID-19: A Backcasting Approach with Monte Carlo Methods

Immunoregulation in human malaria: the challenge of understanding asymptomatic infection

Quantification of bird-to-bird and birdto-human infections during 2013 novel H7N9 avian influenza outbreak in China

Ebola outbreak in West Africa: real-time estimation and multiple-wave prediction

The scale and dynamics of COVID-19 epidemics across Europe

Estimation of the basic reproduction number of novel coronavirus (COVID-19) in Bangladesh: A 65-day outbreak datadriven analysis

African Countries by population

Modelling of reproduction number for COVID-19 in India and high incidence states

Basic reproduction number and predicted trends of coronavirus disease 2019 epidemic in the mainland of China

Richards model: a simple procedure for real-time prediction of outbreak severity in Modeling and dynamics of infectious diseases

A flexible growth function for empirical use

The SIR model and the foundations of public health

The parameter identification problem for SIR epidemic models: identifying unreported cases

A comparison study of Zika virus outbreaks in French Polynesia, Colombia and the State of Bahia in Brazil

Prevention and control of Zika as a mosquito-borne and sexually transmitted disease: a mathematical modeling analysis

Vespignani A . Spread of Zika virus in the Americas

Estimate of the reproduction number of the 2015 Zika virus outbreak in

Barranquilla, Colombia, and estimation of the relative role of sexual transmission

Mathematical models in population biology and epidemiology

Modeling the spread of Middle East respiratory syndrome coronavirus in Saudi Arabia

Predicting COVID-19 spread in the face of control measures in West Africa

Coronavirus pandemic: A predictive analysis of the peak outbreak epidemic in South Africa, Turkey, and Brazil

Prediction models for diagnosis and prognosis of covid-19 infection: systematic review and critical appraisal

Time series modelling to forecast the confirmed and recovered cases of COVID-19

Prediction models for diagnosis and prognosis in Covid-19

Extended SIR prediction of the epidemics trend of COVID-19 in Italy and compared with Hunan

Real-time estimation and prediction of mortality caused by COVID-19 with patient information based algorithm

Discussion: the Kermack-McKendrick epidemic threshold theorem

Predicting turning point, duration and attack rate of COVID-19 outbreaks in major Western countries

A discrete stochastic model of the COVID-19 outbreak: Forecast and control

COVID-19 pandemic in west Africa

Multidisciplinary research priorities for the COVID-19 pandemic: a call for action for mental health science

Preparedness and vulnerability of African countries against importations of COVID-19: a modelling study

Looming threat of COVID-19 infection in Africa: act collectively, and fast

Africa in the Path of Covid-19

Why is it difficult to accurately predict the COVID-19 epidemic?

Data-Based Analysis, Modelling and Forecasting of the novel Coronavirus (2019-nCoV) outbreak. medRxiv

Epidemiological and clinical features of the 2019 novel coronavirus outbreak in China. medRxiv

Prediction of Peak and Termination of Novel Coronavirus Covid-19 Epidemic in Iran. medRxiv

Estimating epidemic exponential growth rate and basic reproduction number

Public health criteria to adjust public health and social measures in the context of COVID-19. Annex to Considerations in adjusting public health and social measures in the context of COVID-19

Global health observatory data

COVID-19 Patient Health Prediction Using Boosted Random Forest Algorithm

Using Supervised Machine Learning and Empirical Bayesian Kriging to reveal Correlates and Patterns of COVID-19 Disease outbreak in sub-Saharan Africa: Exploratory Data Analysis. Available at SSRN 3580721

Modelling for prediction of the spread and severity of COVID-19 and its association with socioeconomic factors and virus types. medRxiv

Early dynamics of transmission and control of COVID-19: a mathematical modelling study. LANCET INFECT DIS

Time-dependent and time-independent SIR models applied to the COVID-19 outbreak in Argentina

On the use of growth models for forecasting epidemic outbreaks with application to COVID-19 data

Quantifying undetected COVID-19 cases and effects of containment measures in Italy

Fitting dynamic models to epidemic outbreaks with quantified uncertainty: A primer for parameter uncertainty, identifiability, and forecasts

Coronavirus Pandemic (COVID-19)

Computer Software

Effects of Population Density on the Spread of Disease

Effects of population density on the spread of disease

Average detection rate of SARS-CoV-2 infections is estimated around six percent