Abstract
In this paper, it is proposed and analyzed a new mathematical model and that is developed on the basis of some reasonable modification made to the standard epidemic model. The impact of immigration, treatment and the effect of vaccination are included in the model. The basic reproduction number is derived using the next generation matrix method. Disease free equilibrium point is found and endemic equilibrium state is identified. Numerical simulation study is conducted using <i>ode 45</i> of MATLAB. It has been shown that the solution is positive and bounded. Algebraic expression for the reproduction number is constructed. Equilibrium points are identified and their stability analysis is carried out. It is pointed out that the disease dies out if the immigration of the infected dogs is controlled and the vaccination and the treatments are improved. Otherwise, the disease spreads rapidly in the dog population and it becomes an epidemic. Further, it is also pointed out that the impact of infective immigrants on the spread of dog rabies is positive and additive. The details are presented and discussed in the text.
Highlights
In the present world, immigration has become unavoidable activity but it poses a significant risk for disease propagation in every population in general and rabies among dog populations in particular
The dog rabies disease has been in existence for more than three thousand years and it is the oldest infectious disease known to medical science
The whole dog populations categorized into four classes: (i) Susceptible class refers to the healthy dogs that have not yet caught the rabies virus but are likely to contract the disease (ii) Exposed class refers to the dogs that have been bitten by infected dogs but are not made up to be infectious (iii) Infective class refers to the dogs infected with rabies virus and are contagious make up and (iv) the removed class constitute dogs which have died from the infection
Summary
Immigration has become unavoidable activity but it poses a significant risk for disease propagation in every population in general and rabies among dog populations in particular. Rabies virus is transmitted in the form of saliva through the bite of an infected animal. Dog rabies is estimated to cause 24,000 human deaths per year in Africa, while Africa is the second continent mostly affected by the disease. The main cause of transmission of rabies to human in Africa is by a bite of a rabid dog. Transmission of rabies: Any warm – blooded animals including humans may become infected with the rabies virus and develop symptoms. During the rabies incubation period, a bite by the infected animal does not carry a risk of rabies because the virus is not yet in the saliva. If a dog or a person is bitten by a rabid animal and has not yet experienced symptoms, there is an extremely effective post – exposure treatment. These spatially explicit models may not have provided much improvement over the earliest ODE models used 30 years ago, because early in the epidemic, detailed temporal history was not yet available and spatial resolution was limited to densities of individuals within large regions [4]
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