Numerical and theoretical analysis of Rabies model under the harmonic mean type incidence rate

In recent years, rabies virus transmission has affected the community widely. Therefore, the study of this deadly virus transmission acquires a significant place in the epidemic spreading. One way to know about the inner sight of such diseases is to consider them mathematically. In this research, we develop a mathematical model for rabies transmission under harmonic mean type incidence rate and consider its qualitative behavior. Using the Next Generation matrix technique, we have derived the threshold number R-0 for the given model. Local and Global stabilities for the disease-free equilibrium are discussed using the Castillo-Chavez method. We have further derived the conditions under which R-0 > 1 and have shown that the model is locally and globally stable at an endemic equilibrium point. For stability, a geometrical approach which is the generalization of Lyapunov theory is used by using a third additive compound matrix. The sensitivity analysis of the basic reproductive number R-0 is carried out and some important parameters are discussed in the last section.