Mathematical Model for Transmission of Leptospirosis

Mathematical model is a very useful tool to understand and analyse the dynamics of diseases. This paper formulates a non-linear mathematical model which investigates the Mathematical Model for Transmission of Leptospirosis by dividing the population into 6 groups. The human population is divided into three subgroups such as Susceptible (S_h) , Infectious (I_h ) ,Recovered (R_h) and Vaccination(V_h ).The rat is divided into two subgroups such as Susceptible (S_r ) and Infectious (I_r ) . The model exhibits two equilibriums: disease-free and endemic equilibriums. The numerical simulation show that if the basic reproductive number is less than unity, the disease-free equilibrium is locally asymptotically stable. On the contrary, if a basic reproduction number is greater than unity, the endemic equilibrium is locally
asymptotically stable