The outbreak of novel coronavirus-caused pneumonia (COVID-19) in Wuhan has attracted worldwide attention. Here, we propose a generalized SEIR model to analyze this epidemic. Based on the public data of National Health Commission of China from Jan. 20th to Feb. 9th, 2020, we reliably estimate key epidemic parameters and make predictions on the inflection point and possible ending time for 5 different regions. According to optimistic estimation, the epidemics in Beijing and Shanghai will end soon within two weeks, while for most part of China, including the majority of cities in Hubei province, the success of anti-epidemic will be no later than the middle of March. The situation in Wuhan is still very severe, at least based on public data until Feb. 15th. We expect it will end up at the beginning of April. Moreover, by inverse inference, we find the outbreak of COVID-19 in Mainland, Hubei province and Wuhan all can be dated back to the end of December 2019, and the doubling time is around two days at the early stage.
We present Coronavirus disease 2019 (COVID-19) statistics in China dataset: daily statistics of the COVID-19 outbreak in China at the city/county level. For each city/country, we include the six most important numbers for epidemic research: daily new infections, accumulated infections, daily new recoveries, accumulated recoveries, daily new deaths, and accumulated deaths. We cross validate the dataset and the estimate error rate is about 0.04%. We then give several examples to show how to trace the spreading in particular cities or provinces, and also contrast the development of COVID-19 in al…
A model of reactive social distancing in epidemics is proposed, in which the infection rate changes with the number infected. The final-size equation for the total number that the epidemic will infect can be derived analytically, as can the peak infection proportion. This model could assist planners during for example the COVID-19 pandemic.
To model the evolution of diseases with extended latency periods and the presence of asymptomatic patients like COVID-19, we define a simple discrete time stochastic SIR-type epidemic model. We include both latent periods as well as the presence of quarantine areas, to capture the evolutionary dynamics of such diseases.
By using the public data from Jan. 20 to Feb. 11, 2020, we perform data-driven analysis and forecasting on the COVID-19 epidemic in mainland China, especially Hubei province. Our results show that the turning points of the daily infections are predicted to be Feb. 6 and Feb. 1, 2020, for Hubei and China other than Hubei, respectively. The epidemic in China is predicted to end up after Mar. 10, 2020, and the number of the total infections are predicted to be 51600. The data trends reveal that quick and active strategies taken by China to reduce human exposure have already had a good impact on t…
Social distancing and lockdown are the two main non-pharmaceutical interventions being used by the UK government to contain and control the COVID-19 epidemic; these are being applied uniformly across the entire country, even though the results of the Imperial College report by Ferguson et al show that the impact of the infection increases sharply with age. This paper develops a variant of the workhorse SIR model for epidemics, where the population is classified into a number of age groups. This allows us to understand the effects of age-dependent controls on the epidemic, and explore possible …
We model the COVID-19 coronavirus epidemic in China. We use early reported case data to predict the cumulative number of reported cases to a final size. The key features of our model are the timing of implementation of major public policies restricting social movement, the identification and isolation of unreported cases, and the impact of asymptomatic infectious cases.
The goal of this work is to analyse the effects of control policies for the coronavirus (COVID-19) epidemic in Brazil. This is done by considering an age-structured SEIR model with a quarantine class and two types of controls. The first one studies the sensitivity with regard to the parameters of the basic reproductive number R0 which is calculated by the next generation method. The second one evaluates different quarantine strategies by comparing their relative total number of deaths.
Since the first outbreak of the COVID-19 epidemic at the end of 2019, data has been made available on the number of infections, deaths and recoveries for all countries of the World, and that data can be used for statistical analysis. The primary interest of this paper is how well the logistic equation can predict the outcome of COVID-19 epidemic in any regions of the World assuming that the methodology of the testing process, namely the data collection method and social behavior is not changing over the course of time. Besides the social relevance, this study has two scientific purposes: we in…
Nowadays, the epidemic of COVID-19 in China is under control. However, the epidemic are developing rapidly around the world. Due to the normal migration of population, China is facing high risk from imported cases. The potential specific medicine and vaccine is still in the process of clinical trials. Currently, controlling the impact of imported cases is the key to prevent new outbreak of COVID-19 in China. In this paper, we propose two impulsive systems to describe the impact of multilateral imported cases of COVID-19. Based on the published data, we simulate and discussed the epidemic trend…
We present a compartmental SEIAR model of epidemic spread as a generalization of the SEIR model. We believe that the asymptomatic infectious cohort is an omitted part of the understanding of the epidemic dynamics of disease COVID-19. We introduce and derive the basic reproduction number as the weighted arithmetic mean of the basic reproduction numbers of the symptomatic and asymptomatic cohorts. Since the asymptomatic subjects people are not detected, they can spread the disease much longer, and this increases the COVID-19 $R_0$ up to around 9. We show that European epidemic outbreaks in vario…
The goal of this work is to consider widespread use of face masks as a non-pharmaceutical control strategy for the Covid-19 pandemic. A SEIR model that divides the population into individuals that wear masks and those that do not is considered. After calculating the basic reproductive number by a next generation approach, a criterion for determining when an epidemic can be prevented by the use of masks only and the critical percentage of mask users for disease prevention in the population are derived. The results are then applied to real world data from the United States, Brazil and Italy.
Objectives: We aim to assess the impact of temperature and relative humidity on the transmission of COVID-19 across communities after accounting for community-level factors such as demographics, socioeconomic status, and human mobility status. Design: A retrospective cross-sectional regression analysis via the Fama-MacBeth procedure is adopted. Setting: We use the data for COVID-19 daily symptom-onset cases for 100 Chinese cities and COVID-19 daily confirmed cases for 1,005 U.S. counties. Participants: A total of 69,498 cases in China and 740,843 cases in the U.S. are used for calculating the …
The paper deals with a modeling of the ongoing epidemic caused by Coronavirus disease 2019 (COVID-19) on the closed territory of the Republic of Croatia. Using the official public information on the number of confirmed infected, recovered and deceased individuals, the modified SEIR compartmental model is developed to describe the underlying dynamics of the epidemic. Fitted modified SEIR model provides the prediction of the disease progression in the near future, considering strict control interventions by means of social distancing and quarantine for infected and at-risk individuals introduced…
The aim of the paper is to describe two models of Covid-19 infection dynamics. For this purpose a special class of branching processes with two types of individuals is considered. These models are intended to use only the observed daily statistics to estimate the main parameter of the infection and to give a prediction of the mean value of the non-observed population of the infected individuals. Similar problems are considered also in the case when the processes admit an immigration component. This is a serious advantage in comparison with other more complicated models where the officially rep…
We measure the effect of different public health regulations to the spread of COVID-19, based on a SEIRA model -- a SEIR model including asymptomatic transmissions. The cumulative confirmed cases and death show nonlinear positive relationship with the value of asymptomatic rate. Based on this model, we analyze the inhibit effects to COVID-19 of three types of public health policies, i.e. isolation of laboratory confirmed cases, general personal protection and quarantine (lock-down). The simulations conclude that the isolation display limited effects to the asymptomatic viral carriers. The gene…
In this research, we study the propagation patterns of epidemic diseases such as the COVID-19 coronavirus, from a mathematical modeling perspective. The study is based on an extensions of the well-known susceptible-infected-recovered (SIR) family of compartmental models. It is shown how social measures such as distancing, regional lockdowns, quarantine and global public health vigilance, influence the model parameters, which can eventually change the mortality rates and active contaminated cases over time, in the real world. As with all mathematical models, the predictive ability of the model …
The control of Covid 19 epidemics by public health policy in Italy during the first and the second epidemic waves has been driven by using reproductive number Rt(t) to identify the supercritical (percolative), the subcritical (arrested), separated by the critical regime. Here we show that to quantify the Covid-19 spreading rate with containment measures (CSRwCM) there is a need of a 3D expanded parameter space phase diagram built by the combination of Rt(t) and doubling time Td(t). In this space we identify the dynamics of the Covid-19 dynamics Italy and its administrative Regions. The supercr…
We model further development of the COVID-19 epidemic in the UK given the current data and assuming different scenarios of handling the epidemic. In this research, we further extend the stochastic model suggested in \cite{us} and incorporate in it all available to us knowledge about parameters characterising the behaviour of the virus and the illness induced by it. The models we use are flexible, comprehensive, fast to run and allow us to incorporate the following: -time-dependent strategies of handling the epidemic; -spatial heterogeneity of the population and heterogeneity of development of …
Objective: To conduct an early estimation of the Basic Reproduction Number (BRN) induced by government interference, and to project resulting day to day number of in-patients, ICU-patients and cumulative number of deaths in a Danish setting. Method: We used the Kermack and McKendrick model with varying basic reproduction number to estimate number infected and age stratified percentages to estimate number of in-patients, ICU-patients and cumulative number of deaths. Changes in basic reproduction number was estimated based on current in-patient numbers. Results: The basic reproductive number in …
COVID-19 epidemics in Japan and Tokyo were analyzed by a fundamental equation of the dynamic phase transition. As a result, the epidemic was found to be in good agreement with the random nucleation and linear growth model suggesting that the epidemic between March 13, 2020 and May 22, 2020 was simply rate-limited by the three constant-parameters: the initial susceptible, domain growth rate, and nucleation decay constant. This model provides a good predictor of the epidemic because it consists of one equation and the initial specific plot is linear.
We study Susceptible-Exposed-Asymptomatic-Infectious-Recovered (SEAIR) epidemic spreading model of COVID-19. It captures two important characteristics of the infectiousness of COVID-19: delayed start and its appearance before onset of symptoms, or even with total absence of them. The model is theoretically analyzed in continuous-time compartmental version and discrete-time version on random regular graphs and complex networks. We show analytically that there are relationships between the epidemic thresholds and the equations for the susceptible populations at the endemic equilibrium in all thr…
A pandemic caused by a new coronavirus (COVID-19) has spread worldwide, inducing an epidemic still active in Argentina. In this chapter, we present a case study using an SEIR (Susceptible-Exposed-Infected-Recovered) diffusion model of fractional order in time to analyze the evolution of the epidemic in Buenos Aires and neighboring areas (Región Metropolitana de Buenos Aires, (RMBA)) comprising about 15 million inhabitants. In the SEIR model, individuals are divided into four classes, namely, susceptible (S), exposed (E), infected (I) and recovered (R). The SEIR model of fractional order allows…
We use a simple SIR-like epidemic model which integrates known age-contact patterns for the United States to model the effect of age-targeted mitigation strategies for a COVID-19-like epidemic. We find that, among strategies which end with population immunity, strict age-targeted mitigation strategies have the potential to greatly reduce mortalities and ICU utilization for natural parameter choices.
The recent epidemic of Coronavirus (COVID-19) that started in China has already been "exported" to more than 140 countries in all the continents, evolving in most of them by local spreading. In this contribution we analyze the trends of the cases reported in all the Chinese provinces, as well as in some countries that, until March 15th, 2020, have more than 500 cases reported. Notably and differently from other epidemics, the provinces did not show an exponential phase. The data available at the Johns Hopkins University site seem to fit well an algebraic sub-exponential growing behavior as was…
A configuration model for epidemic spread, based on a scale-free network, is introduced. We obtain the analytical solutions describing both unstable and stable dynamics of the epidemic spreading, and demonstrate how these regimes can interchange during the epidemic. We apply the model to the COVID-19 case and demonstrate the predictive features of our model.
The initial cluster of severe pneumonia cases that triggered the 2019-nCoV epidemic was identified in Wuhan, China in December 2019. While early cases of the disease were linked to a wet market, human-to-human transmission has driven the rapid spread of the virus throughout China. The ongoing outbreak presents a challenge for modelers, as limited data are available on the early growth trajectory, and the epidemiological characteristics of the novel coronavirus are yet to be fully elucidated. We provide timely short-term forecasts of the cumulative number of confirmed reported cases in Hubei pr…
The initial surge of the COVID-19 pandemic hit Guatemala on March 2020. On a country scale, the epidemic has undergone a fairly well-known and distinguishable initial phase, reaching its peak on mid July 2020. However, the detailed picture is more involved and reflects inter-regional variations in the epidemic dynamics, presumably grounded on socio-demographic, connectivity, and human mobility factors. Classifying the regional epidemic curves and identifying the major hubs of regional COVID-19 spread can contribute towards defining an evidence-based risk map for future outbreaks of infectious …
Recent literature has suggested that climate conditions have considerably significant influences on the transmission of coronavirus COVID-19. However, there is a lack of comprehensive study that investigates the relationships between multiple weather factors and the development of COVID-19 pandemic while excluding the impact of social factors. In this paper, we study the relationships between six main weather factors and the infection statistics of COVID-19 on 250 cities in Mainland China. Our correlation analysis using weather and infection statistics indicates that all the studied weather fa…
We show how the standard field theoretical language based on creation and annihilation operators may be used for a straightforward derivation of an SIR-type stochastic model for COVID-19 epidemic, from which we obtain the time evolution of the mean number of infectious (active cases) and deceased individuals. In order to capture the effects of lockdown and social distancing, we use a time-dependent infection rate. The results are in good agreement with the data for three different waves of epidemic activity in South Korea.
While COVID-19 is rapidly propagating around the globe, the need for providing real-time forecasts of the epidemics pushes fits of dynamical and statistical models to available data beyond their capabilities. Here we focus on statistical predictions of COVID-19 infections performed by fitting asymptotic distributions to actual data. By taking as a case-study the epidemic evolution of total COVID-19 infections in Chinese provinces and Italian regions, we find that predictions are characterized by large uncertainties at the early stages of the epidemic growth. Those uncertainties significantly r…
Due to modern transportation networks (airplanes, cruise ships, etc.) an epidemic in a given country or city may be triggered by the arrival of external infected agents. Posterior government quarantine policies are usually taken in order to control the epidemic growth. We formulate a minimal epidemic evolution model that takes into account these components. The previous and posterior evolutions to the quarantine policy are modeled in a separate way by considering different complexities parameters in each stage. Application of this model to COVID-19 data in different countries is implemented. E…
The outbreak of novel coronavirus (2019-nCoV) in China has caused a viral epidemic affecting tens of thousands of persons. Though the danger of this epidemic is evident, the statistical analysis of data offered in this paper indicates that the increase in new cases in China will stabilize in the coming days or weeks. Our forecast could serve to evaluate risks and control the evolution of this disease.
Mexico, like the rest of the world, is currently facing the The COVID-19 pandemic. Given the size of its territory, the efforts to contain the disease have involved both national and regional measures. For this work, the curves of daily new cases of each municipality reported by the federal government were compared. We found that 114 municipalities form a large network of statistically dependent epidemic phenomena. Based on the network's modular structure, these 114 municipalities can be split into four distinct communities of coordinated epidemic phenomena. These clusters are not limited by g…
In this paper, based on the Akaike information criterion, root mean square error and robustness coefficient, a rational evaluation of various epidemic models/methods, including seven empirical functions, four statistical inference methods and five dynamical models, on their forecasting abilities is carried out. With respect to the outbreak data of COVID-19 epidemics in China, we find that before the inflection point, all models fail to make a reliable prediction. The Logistic function consistently underestimates the final epidemic size, while the Gompertz's function makes an overestimation in …
In this study, we analyze the effectiveness of measures aimed at finding and isolating infected individuals to contain epidemics like COVID-19, as the suppression induced over the effective reproduction number. We develop a mathematical model to compute the relative suppression of the effective reproduction number of an epidemic that such measures produce. This outcome is expressed as a function of a small set of parameters that describe the main features of the epidemic and summarize the effectiveness of the isolation measures. In particular, we focus on the impact when a fraction of the popu…
We propose a stochastic SIR model, specified as a system of stochastic differential equations, to analyse the data of the Italian COVID-19 epidemic, taking also into account the under-detection of infected and recovered individuals in the population. We find that a correct assessment of the amount of under-detection is important to obtain reliable estimates of the critical model parameters. Moreover, a single SIR model over the whole epidemic period is unable to correctly describe the behaviour of the pandemic. Then, the adaptation of the model in every time-interval between relevant governmen…
In December 2019, COVID-19 were detected in Wuhan City, Hubei Province of China. SARS-CoV-2 rapidly spread to the whole Chinese mainland with the people during the Chinese Spring Festival Travel Rush. As of 19 February 2020, 74576 confirmed cases of COVID-19 had been reported in Chinese Mainland. What kind of cities have more confirmed cases, and is there any relationship between GDP and confirmed cases? In this study, we explored the relationship between the confirmed cases of COVID-19 and GDP at the prefectural-level, found a positive correlation between them. This finding warns high GDP are…
An analysis of the COVID-19 epidemic is proposed on the basis of the epiMOX dashboard (publicly accessible at https://www.epimox.polimi.it) that deals with data of the epidemic trends and outbreaks in Italy from late February 2020. Our analysis provides an immediate appreciation of the past epidemic development, together with its current trends by fostering a deeper interpretation of available data through several critical epidemic indicators. In addition, we complement the epiMOX dashboard with a predictive tool based on an epidemiological compartmental model, named SUIHTER, for the forecast …
This is work in progress. We make it accessible hoping that people might find the idea useful. We propose a discrete, recursive 5-compartment model for the spread of epidemics, which we call {\em SEPIR-model}. Under mild assumptions which typically are fulfilled for the Covid-19 pandemic it can be used to reproduce the development of an epidemic from a small number of parameters closely related to the data. We demonstrate this at the development in Germany and Switzerland. It also allows model predictions assuming nearly constant reproduction numbers. Thus it might be a useful tool for sheddin…
COVID-19 is a new type of coronavirus disease which is caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). It originated in China in the month of December 2019 and quickly started to spread within the country. On 31st December 2019, it was first reported to country office of World Health Organization (WHO) in China. Since then, it has spread to most of the countries around the globe. However, there has been a recent rise in trend in believing that it would go away during summer days, which has not yet been properly investigated. In this paper, relationship of daily number o…
In a given country, the cumulative death toll of the first wave of the COVID-19 epidemic follows a sigmoid curve as a function of time. In most cases, the curve is well described by the Gompertz function, which is characterized by two essential parameters, the initial growth rate and the decay rate as the first epidemic wave subsides. These parameters are determined by socioeconomic factors and the countermeasures to halt the epidemic. The Gompertz model implies that the total death toll depends exponentially, and hence very sensitively, on the ratio between these rates. The remarkably differe…
Based on the SEIR model and the modeling of urban transportation networks, a general-purpose simulator for the spread of epidemics in Chinese cities is built. The Chinese public transportation system between over 340 prefectural-level cities is modeled as a multi-layer bi-partite network, with layers representing different means of transportation (airlines, railways, sail routes and buses), and nodes divided into two categories (central cities, peripheral cities). At each city, an open-system SEIR model tracks the local spread of the disease, with population in- and out-flow exchanging with th…
Coronavirus disease (COVID-2019) is a severe ongoing novel pandemic that is spreading quickly across the world. Italy, that is widely considered one of the main epicenters of the pandemic, has registered the highest COVID-2019 death rates and death toll in the world, to the present day. In this article I estimate an autoregressive integrated moving average (ARIMA) model to forecast the epidemic trend over the period after April 4, 2020, by using the Italian epidemiological data at national and regional level. The data refer to the number of daily confirmed cases officially registered by the It…
While understanding of periodic recurrent waves of Covid-19 epidemics would aid to combat the pandemics, quantitative analysis of data over a two years period from the outbreak, is lacking. The complexity of Covid-19 recurrent waves is related with the concurrent role of i) the containment measures enforced to mitigate the epidemics spreading ii) the rate of viral gene mutations, and iii) the variable immune response of the host implemented by vaccination. This work focuses on the effect of massive vaccination and gene variants on the recurrent waves in a representative case of countries enfor…
Calibration of a SIR (Susceptibles-Infected-Recovered) model with official international data for the COVID-19 pandemics provides a good example of the difficulties inherent the solution of inverse problems. Inverse modeling is set up in a framework of discrete inverse problems, which explicitly considers the role and the relevance of data. Together with a physical vision of the model, the present work addresses numerically the issue of parameters calibration in SIR models, it discusses the uncertainties in the data provided by international authorities, how they influence the reliability of c…
On the base of logic discrete equations system mathematical modeling of COVID-19 epidemic spread was carried out in the world and in the countries with the largest number of infected people such as the USA, Brasil, Russia and India in the first half of 2020. It was shown that for the countries with strong restrictive measures the spread of COVID-19 fit on a single wave with small capacity as for a number of countries with violation of restrictive measures the spread of the epidemic fit on a waves superposition. For countries with large population mixing, the spread of the epidemic today also f…
The discovery of SARS-CoV-2, the responsible virus for the Covid-19 epidemic, has sparked a global health concern with many countries affected. Developing models that can interpret the epidemic and give common trend parameters are useful for prediction purposes by other countries that are at an earlier phase of the epidemic; it is also useful for future planning against viral respiratory diseases. One model is developed to interpret the fast-growth phase of the epidemic and another model for an interpretation of the entire data set. Both models agree reasonably with the data. It is shown by th…
The ongoing Coronavirus Disease 2019 (COVID-19) pandemic threatens the health of humans and causes great economic losses. Predictive modelling and forecasting the epidemic trends are essential for developing countermeasures to mitigate this pandemic. We develop a network model, where each node represents an individual and the edges represent contacts between individuals where the infection can spread. The individuals are classified based on the number of contacts they have each day (their node degrees) and their infection status. The transmission network model was respectively fitted to the re…
Governments around the world have implemented preventive measures against the spread of the coronavirus disease (COVID-19). In this study, we consider a multivariate discrete-time Markov model to analyze the propagation of COVID-19 across 33 provincial regions in China. This approach enables us to evaluate the effect of mobility restriction policies on the spread of the disease. We use data on daily human mobility across regions and apply the Bayesian framework to estimate the proposed model. The results show that the spread of the disease in China was predominately driven by community transmi…
Can public social media data be harnessed to predict COVID-19 case counts? We analyzed approximately 15 million COVID-19 related posts on Weibo, a popular Twitter-like social media platform in China, from November 1, 2019 to March 31, 2020. We developed a machine learning classifier to identify "sick posts," which are reports of one's own and other people's symptoms and diagnosis related to COVID-19. We then modeled the predictive power of sick posts and other COVID-19 posts on daily case counts. We found that reports of symptoms and diagnosis of COVID-19 significantly predicted daily case cou…
There were 27 novel coronavirus pneumonia cases found in Wuhan, China in December 2019, named as 2019-nCoV temporarily and COVID-19 formally by WHO on 11 February, 2020. In December 2019 and January 2020, COVID-19 has spread in large scale among the population, which brought terrible disaster to the life and property of the Chinese people. In this paper, we will first analyze the feature and pattern of the virus transmission, and discuss the key impact factors and uncontrollable factors of epidemic transmission based on public data. Then the virus transmission can be modelled and used for the …
In order to investigate the effectiveness of lockdown and social distancing restrictions, which have been widely carried out as policy choice to curb the ongoing COVID-19 pandemic around the world, we formulate and discuss a staged and weighed networked system based on a classical SEAIR epidemiological model. Five stages have been taken into consideration according to four-tier response to Public Health Crisis, which comes from the National Contingency Plan in China. Staggered basic reproduction number has been derived and we evaluate the effectiveness of lockdown and social distancing policie…
Started in Wuhan, China, the COVID-19 has been spreading all over the world. We calibrate the logistic growth model, the generalized logistic growth model, the generalized Richards model and the generalized growth model to the reported number of infected cases for the whole of China, 29 provinces in China, and 33 countries and regions that have been or are undergoing major outbreaks. We dissect the development of the epidemics in China and the impact of the drastic control measures both at the aggregate level and within each province. We quantitatively document four phases of the outbreak in C…
We review epidemiological models for the propagation of the COVID-19 pandemic during the early months of the outbreak: from February to May 2020. The aim is to propose a methodological review that highlights the following characteristics: (i) the epidemic propagation models, (ii) the modeling of intervention strategies, (iii) the models and estimation procedures of the epidemic parameters and (iv) the characteristics of the data used. We finally selected 80 articles from open access databases based on criteria such as the theoretical background, the reproducibility, the incorporation of interv…
We demonstrate that the epidemic renormalisation group approach to pandemics provides an effective and simple way to investigate the dynamics of disease transmission and spreading across different regions of the world. The framework also allows for reliable projections on the impact of travel limitations and social distancing measures on global epidemic spread. We test and calibrate it on reported cases while unveiling the mechanism that governs the delay in the relative peaks of newly infected cases among different regions of the globe. We discover that social distancing measures are more eff…
In this paper we develop a predictive model for the spread of COVID-19 infection at a provincial (i.e. EU NUTS-3) level in Italy by using official data from the Italian Ministry of Health integrated with data extracted from daily official press conferences of regional authorities and from local newspaper websites. This integration is mainly concerned with COVID-19 cause specific death data which are not available at NUTS-3 level from open official data data channels. An adjusted time-dependent SIRD model is used to predict the behavior of the epidemic, specifically the number of susceptible, i…
