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A mathematical modeling of rabies with vaccination and culling

Rabies is a fatal contagious disease but preventable. It is a major public health problem in developing countries. Most of the rabies deaths around the world are caused by dog bites. If a person does not receive appropriate treatment after being exploded to rabies, the virus can damage the brain resulting in death. Since most of the deaths due to the transmission from dogs to humans, therefore, in this study, we will formulate a mathematical model that describes the dynamics of rabies virus transmission between dogs and humans. Also, we conduct both epidemic and endemic analysis. Optimal control theory is applied to seek cost-effective solutions for time-dependent vaccination and culling strategies against rabies outbreaks. Our results show that using vaccination during rabies outbreaks at the very beginning of the onset and culling infected dogs can reduce the number of infections significantly.