A Novel Mathematical Model and Homotopy Perturbation Method Analyzing the Effects of Saturated Incidence and Treatment Rate on COVID-19 Eradication

Abstract

Saturated incidence rates and treatment responses are essential in epidemiology and clinical research. They signify peak event occurrences in a population, aiding in disease understanding and intervention planning. This study proposes a mathematical model of COVID-19, focusing on the impact of saturated incidence rates and treatment responses on its dynamical transmission. Via qualitative analysis, the existence and uniqueness of the model’s solution are verified, a positive invariant region is established, and the local stability analysis highlights the model’s resilience to minor perturbations. The model solution is obtained utilizing the homotopy perturbation method, and simulations with Maple 18 software reveal that increasing treatment intensity might not result in significant additional decrease in the number of infections, particularly in situations where the spread of infection is uncontrolled. Thus, the finding underscores the need to refine treatment strategies through a tailored approach and to optimize preventive measures.