Epidemics modeling

Abstract

Introduction. Due to the spread of COVID-19 in the world, mathematical modeling of epidemiological processes is an important and relevant scientific problem. There are many models describing the dynamics of pandemics, such as the standard SIR model, but most of them are deterministic, while in reality, the processes of infecting and recoveries are random in nature. Also, most of the models either do not include the existence of vaccines or medication or do not take into consideration the price of such medication. Sometimes, because of the high price, the widespread use of contemporary medication is impossible, especially in poor countries. In this case, there is a problem of finding a compromise between the purchase of a low amount of medication and a low amount of human deaths as a result of a pandemic. We propose a stochastic model, which describes this situation. The purpose of the paper is to develop a mathematical model corresponding to the minimization of losses from certain pandemics, as well as the analysis of such a model. Results. In this paper, we propose a stochastic model that describes the behavior of an epidemic with a certain amount of medication administered among the population. We present several estimates for the parameters of the epidemic, such as its duration and the total number of infected people at a certain time, given an initial number of infected people. The first two moments of the number of infected people at a given time were found. Furthermore, we found an estimate of the total losses as a result of the pandemic, which includes medication costs and losses from deaths. Several formulas are presented, which simplify the search for the minimal amount of medication needed to minimize the losses. Conclusions. The presented problem and its solution can be used for models of certain epidemics to minimize the medication costs and losses from deaths. Keywords: epidemic, epidemic modeling, loss minimization.