Local Stability of Equilibrium Points of a SIR Mathematical Model of Infectious Diseases

S. A. Egbetade, I.A. Salawu, P.A. Fasanmade

In this paper, we studied a SIR mathematical model of infectious diseases. We formulate a theorem on existence and uniqueness of solutions and establish the proof of the theorem We showed that the model has two equilibrium points: disease-free and endemic equilibrium. Local stability of the equilibrium points was obtained using reliable Jacobian matrices and basic reproduction number (R0). The analysis reveals that the disease- free equilibrium is locally asymptotically stable if R0 <1, the infection is temporalwill disappear with time. On the other hand, if R0 >1, the number of infections rises, an epidemic results and the endemic equilibrium is locally stable.