Stability analysis and numerical simulation of rabies spread model with delay effects

In this article, a delay differential equations model is constructed to observe the spread of rabies among human and dog populations by considering two delay effects on incubation period and vaccine efficacy. Other parameters that affect the spread of rabies are also analyzed. Using the basic reproduction number, it is shown that dog populations and the two delays gives a significant effect on the spread of rabies among human and dog populations. The existence of two delays causes the system to experience Transcritical bifurcation instead of Hopf bifurcation. The numerical simulation shows that depending only on one control method is not enough to reduce or eradicate rabies within the dog populations; instead, it requires several combined strategies, such as increasing dog vaccinations, reducing contact with infected dogs, and controlling puppies' birth. The spread within the human population will be reduced if the spread within the dog population is reduced.