Evolution of COVID-19 Disease Using a One Prey-Two Predator Model

Abstract

Mathematical modeling is used to understand the dynamics of transmission of infectious diseases such as COVID-19, SARS, Ebola, and Dengue among populations. In this work, a one prey-two predator model has been developed to understand the underlying dynamics of COVID-19 disease transmission. We consider the infected, recovered, and death classes with the fact that an infected person can be transformed into the recovered or death group assuming that the infected ones are the prey, and the other two populations are the two predators in the one prey-two predator model. It was found that the proposed model has four equilibrium points; the vanishing equilibrium point (E_0), recovered and death-free equilibrium point (E_1), infected and recovered population-free equilibrium point (E_2), and the death-free equilibrium point (E_3). Stability analysis of the equilibrium points shows that all the other equilibrium points are locally stable. Global asymptotic stability of the recovered and death-free equilibrium point, infected and recovered free and death-free equilibrium point are also analyzed. Moreover, the existence and uniqueness of the solutions were proved. The parameters for the model are estimated from a data set that consists of the total number of infected, recovered, and death classes at a zone for the first 6 months of the year 2020 using the Nelder-Mead optimization method. During the first 6 months, the infected population increases at a higher rate, the recovered population, and the death class increase at a lower rate. However, some modifications to the system are needed. In future work, measures such as health precautions, vaccinations are needed to be considered to formulate the mathematical model and estimate parameters.