Global stability of the dynamics of a new model of coronavirus transmission with viruses in the environment
Abstract
In the present study, we develop a novel mathematical model for COVID-19 transmission by explicitly incorporating the influence of viruses in the environment. Epidemiological evidence suggests that regions with high environmental viral concentration tend to exhibit higher infection rates, although this factor is often neglected in classical transmission models. To address this limitation, we propose a compartmental model consisting of susceptible individuals, symptomatic infected individuals, asymptomatic infected individuals, recovered individuals, and a distinct compartment representing viruses in the environment. The system dynamics are formulated using ordinary differential equations. The dynamical behavior of the model is investigated by analyzing the equilibrium points and deriving the basic reproduction number $\mathcal {R}_0$. Using Lyapunov’s direct method and LaSalle’s invariance principle, sufficient conditions for the local and global stability of both disease-free and endemic equilibria are established. Conditions for disease extinction and persistence are also derived. Similarly, it is inferred that the presence of viruses in the environment is responsible for disease occurrence and is associated with infection severity and threshold levels. Numerical simulations are performed to validate the analytical results and to illustrate the impact of environmental viral concentration on disease transmission.
