STABILITY ANALYSIS OF A SHIGELLA INFECTION EPIDEMIC MODEL AT ENDEMIC EQUILIBRIUM

Abstract

In this study, we modified continuous mathematical model for the dynamics of shigella outbreak at constant recruitment rate formulated by (Ojaswita et al., 2014). In their model, they partitioned the population into Susceptible (S), Infected (I) and recovered (R) individuals. We incorporated a vaccinated class (V), educated class (G), exposed class (E), asymptomatic (A) hospitalized class (H) and Bacteria class (B) with their corresponding parameters. We analyzed a SVGEAIHRB compartmental nonlinear deterministic mathematical model of shigella epidemic in a community with constant population. Analytical studies were carried out on the model using the method of linearized stability. The basic reproductive number  that governs the disease transmission is obtained from the largest eigenvalue of the next-generation matrix. The endemic equilibrium is computed and proved to be locally and globally asymptotically stable if  and unstable if  . Finally, we simulate the model system in MATLAB and obtained the graphical behavior of the infected compartments. From the simulation, we observed that the shigella infection was eradicated when while it persist in the environment when .