In 2012, G. Zaman et al. [26] investigated the model by considering the interaction of susceptible human with infected vector and disease related death rate in both infected human and vectors. To understand the basic properties of the epidemic model, they first formulated the model in detail and define the parameter involve in the model. To this end, they assumed that S_h (t) represents number of susceptible human at time t ; I_h (t) represents number of human in the population, which is infected from the Leptospirosis disease at time t ; R_h (t) represents number of human in the population which is recovered at time t ; they denoted the total population size by N_h with N_h (t)= S_h (t)+I_h (t)+R_h (t).