Dynamics of Rabies Transmission Model in Human and Dog Populations with Time Delay

Abstract

Rabies is a fatal zoonotic disease caused by a virus through bites or saliva of an infected animal. Dogs are the main reservoir of Rabies and are responsible for most Human cases worldwide. In this research, a delay differential equations model for assessing the effects of controls and time delay as an incubation period on the transmission dynamics of Rabies in human and dog populations is formulated and analyzed. Basic properties of the model as par theories of delay differential equations are established, and the model is well-posed mathematically and biologically. Analysis of the model shows that there is a locally and globally asymptotically stable rabies-free equilibrium whenever the epidemiological threshold (the control reproduction number,) is less than unity. Furthermore, the model has a unique endemic equilibrium point when the control reproduction number, exceeds unity. Time delay is found to have an influence on the endemicity of rabies. Treatment and Vaccination of humans and dogs, coupled with an annual crop of puppies, are imposed to curtail the spread of Rabies in the populations. Numerical experiments are conducted to illustrate the theoretical results and control strategies.

Delay differential equations,  Effective reproduction number,  Equilibria, Rabies, Stability