Stability Analysis of a Modified SEIRS Compartmental Model for Infectious Diseases

Mathematical representations of infectious diseases include compartment-based SEIR and SEIRS models. These models are represented using coupled differential equations that capture the flow of populations from one compartment to another and have been used for several infectious diseases such as HIV/AIDS, tuberculosis, Dengue fever, and COVID-19. This paper presents a modified Susceptible - Exposed - Infected - Recovered - Susceptible (SEIRS) compartment model for infectious diseases such as Influenza and COVID-19. We incorporate the compartments for exposed vaccinated and unvaccinated populations, and those with symptomatic and asymptomatic infections. We represent this model with a set of coupled differential equations and show that this system has, among its equilibrium points, an endemic equilibrium. The existence of the equilibrium points is validated using attractor plots. We derive the conditions for local and global stability of the two equilibrium points and derive the conditions under which the system moves from one state of equilibrium to another by varying two parameters values.