Stability Analysis and Numerical Simulation of Rabies Spread Model with Delay Effects

In this research, a delay differential equations model is constructed to observe the spread of rabies among human and dog population by considering two delay effects on incubation period and vaccine efficacy. Other parameters that affect the spread of rabies are also analyzed. By using the basic reproduction number, it is shown that dog population and the two delays given affect the spread of rabies. Although, using local stability analysis around two equilibria, it is found that both delays given do not affect the stability of disease-free equilibrium and endemic equilibrium. It is discovered using numerical simulation that coupled strategies, such as increasing dog vaccination, reducing contact with infected dogs, and controlling puppies’ birth, are required to eradicate the disease. Numerical simulation is also used to give representation to the analysis result.