STABILITY AND SENSITIVITY ANALYSIS OF A SHIGELLA INFECTION EPIDEMIC MODEL AT DISEASE-FREE 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 to: investigate the existence and uniqueness of solution of the model equations and explore the basic properties of the  model equations (i.e. the positivity and boundedness of solutions of the model). The basic R0 reproductive number that governs the disease transmission is obtained from the largest eigenvalue of the next-generation matrix. The disease-free equilibrium points of the model is computed and proved to be locally and globally asymptotically stable if and unstable if . A sensitivity analysis of the epidemiological model of shigella epidemic is performed in order to determine which model parameters are the most important to disease transmission. Finally, we simulate the model system in MATLAB and obtained the graphical behavior of the variables in the R0  model

1 . From the simulation, we observed that the shigella infection was eradicated when

R0  while it persist in the environment when 1.