A REVIEW ON STABILITY ANALYSIS OF AN SIS EPIDEMIC MODEL WITH DEMOGRAPHY

ABSTRACT This study presents a comprehensive review of the stability analysis of the Susceptible–Infectious–Susceptible (SIS) epidemic model with demographic effects. The SIS model is a fundamental mathematical framework used in epidemiology to describe the transmission dynamics of infectious diseases where recovered individuals do not acquire permanent immunity and can return to the susceptible class. The inclusion of demographic factors such as birth and natural death rates enhances the realism of the model by accounting for population turnover. The review examines the formulation of the SIS model with demography, focusing on the system of differential equations that govern the interactions between susceptible and infectious populations. Key concepts such as the disease-free equilibrium (DFE) and endemic equilibrium are discussed, alongside the basic reproduction number (R₀), which serves as a threshold parameter for disease persistence or eradication. Stability analysis techniques, including linearization and the use of Jacobian matrices, are explored to determine the conditions under which these equilibria are locally and globally stable. Findings from the review indicate that when R₀ < 1, the disease-free equilibrium is stable, leading to the eventual elimination of the disease. Conversely, when R₀ > 1, the endemic equilibrium becomes stable, implying sustained transmission within the population. The study highlights the importance of incorporating demographic factors in epidemic modeling and underscores the relevance of stability analysis in informing public health strategies for disease control and prevention.