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Register a new userAn epidemiological model for the spread of COVID-19: A South African case study
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An epidemiological model is developed for the spread of COVID-19 in South Africa. A variant of the classical compartmental SEIR model, called the SEIQRDP model, is used. As South Africa is still in the early phases of the global COVID-19 pandemic with the confirmed infectious cases not having peaked, the SEIQRDP model is first parameterized on data for Germany, Italy, and South Korea - countries for which the number of infectious cases are well past their peaks. Good fits are achieved with reasonable predictions of where the number of COVID-19 confirmed cases, deaths, and recovered cases will end up and by when. South African data for the period from 23 March to 8 May 2020 is then used to obtain SEIQRDP model parameters. It is found that the model fits the initial disease progression well, but that the long-term predictive capability of the model is rather poor. The South African SEIQRDP model is subsequently recalculated with the basic reproduction number constrained to reported values. The resulting model fits the data well, and long-term predictions appear to be reasonable. The South African SEIQRDP model predicts that the peak in the number of confirmed infectious individuals will occur at the end of October 2020, and that the total number of deaths will range from about 10,000 to 90,000, with a nominal value of about 22,000. All of these predictions are heavily dependent on the disease control measures in place, and the adherence to these measures. These predictions are further shown to be particularly sensitive to parameters used to determine the basic reproduction number. The future aim is to use a feedback control approach together with the South African SEIQRDP model to determine the epidemiological impact of varying lockdown levels proposed by the South African Government.
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COVID-19 is a new pandemic disease that is affecting almost every country with a negative impact on social life and economic activities. The number of infected and deceased patients continues to increase globally. Mathematical models can help in developing better strategies to contain a pandemic. Considering multiple measures taken by African governments and challenging socio-economic factors, simple models cannot fit the data. We studied the dynamical evolution of COVID-19 in selected African countries. We derived a time-dependent reproduction number for each country studied to offer further insights into the spread of COVID-19 in Africa.
We propose a mathematical model to analyze the time evolution of the total number of infected population with Covid-19 disease at a region in the ongoing pandemic. Using the available data of Covid-19 infected population on various countries we formulate a model which can successfully track the time evolution from early days to the saturation period in a given wave of this infectious disease. It involves a set of effective parameters which can be extracted from the available data. Using those parameters the future trajectories of the disease spread can also be projected. A set of differential equations is also proposed whose solutions are these time evolution trajectories. Using such a formalism we project the future time evolution trajectories of infection spread for a number of countries where the Covid-19 infection is still rapidly rising.
This paper is concerned with nonlinear modeling and analysis of the COVID-19 pandemic currently ravaging the planet. There are two objectives: to arrive at an appropriate model that captures the collected data faithfully, and to use that as a basis to explore the nonlinear behavior. We use a nonlinear SEIR (Susceptible, Exposed, Infectious & Removed) transmission model with added behavioral and government policy dynamics. We develop a genetic algorithm technique to identify key model parameters employing COVID19 data from South Korea. Stability, bifurcations and dynamic behavior are analyzed. Parametric analysis reveals conditions for sustained epidemic equilibria to occur. This work points to the value of nonlinear dynamic analysis in pandemic modeling and demonstrates the dramatic influence of social and government behavior on disease dynamics.
In this work, we adapt the epidemiological SIR model to study the evolution of the dissemination of COVID-19 in Germany and Brazil (nationally, in the State of Paraiba, and in the City of Campina Grande). We prove the well posedness and the continuous dependence of the model dynamics on its parameters. We also propose a simple probabilistic method for the evolution of the active cases that is instrumental for the automatic estimation of parameters of the epidemiological model. We obtained statistical estimates of the active cases based the probabilistic method and on the confirmed cases data. From this estimated time series we obtained a time-dependent contagion rate, which reflects a lower or higher adherence to social distancing by the involved populations. By also analysing the data on daily deaths, we obtained the daily lethality and recovery rates. We then integrate the equations of motion of the model using these time-dependent parameters. We validate our epidemiological model by fitting the official data of confirmed, recovered, death, and active cases due to the pandemic with the theoretical predictions. We obtained very good fits of the data with this method. The automated procedure developed here could be used for basically any population with a minimum of extra work. Finally, we also propose and validate a forecasting method based on Markov chains for the evolution of the epidemiological data for up to two weeks.
In late-2020, many countries around the world faced another surge in number of confirmed cases of COVID-19, including United Kingdom, Canada, Brazil, United States, etc., which resulted in a large nationwide and even worldwide wave. While there have been indications that precaution fatigue could be a key factor, no scientific evidence has been provided so far. We used a stochastic metapopulation model with a hierarchical structure and fitted the model to the positive cases in the US from the start of outbreak to the end of 2020. We incorporated non-pharmaceutical interventions (NPIs) into this model by assuming that the precaution strength grows with positive cases and studied two types of pandemic fatigue. We found that people in most states and in the whole US respond to the outbreak in a sublinear manner (with exponent k=0.5), while only three states (Massachusetts, New York and New Jersey) have linear reaction (k=1). Case fatigue (decline in peoples vigilance to positive cases) is responsible for 58% of cases, while precaution fatigue (decay of maximal fraction of vigilant group) accounts for 26% cases. If there were no pandemic fatigue (no case fatigue and no precaution fatigue), total positive cases would have reduced by 68% on average. Our study shows that pandemic fatigue is the major cause of the worsening situation of COVID-19 in United States. Reduced vigilance is responsible for most positive cases, and higher mortality rate tends to push local people to react to the outbreak faster and maintain vigilant for longer time.
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