Epidemiological Characteristics of Generalized COVID-19 Deterministic Disease Model

Abstract

Coronavirus disease 2019 (COVID-19) is an infection that can result in lung issues such as pneumonia and, in extreme situations, the most severe acute respiratory syndrome. COVID-19 is widely investigated by researchers through mathematical models from different aspects. Inspired from the literature, in the present paper, the generalized deterministic COVID-19 model is considered and examined. The basic reproduction number is obtained which is a key factor in defining the nonlinear dynamics of biological and physical obstacles in the study of mathematical models of COVID-19 disease. To better comprehend the dynamical behavior of the continuous model, two unconditionally stable schemes, i.e., mixed Euler and nonstandard finite difference (NSFD) schemes are developed for the continuous model. For the discrete NSFD scheme, the boundedness and positivity of solutions are discussed in detail. The local stability of disease-free and endemic equilibria is demonstrated by constructing Jacobian matrices for NSFD scheme; nevertheless, the global stability of aforementioned equilibria is verified by using Lyapunov functions. Numerical simulations are also presented that demonstrate how both the schemes are effective and suitable for solving the continuous model. Consequently, the outcomes obtained through these schemes are completely according to the solutions of the continuous model.