Mathematical model for the introduction of Wolbachia-infected mosquitoes to stop the spread of Yellow Fever

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In this paper, we model the use of wolbachia-infected aedes aegypti mosquitoes to control the spread of yellow fever. Yellow fever is spread through bites of infected and uninfected aedesaegyptimosquitoes.The model, which is a system of non-linear ordinary differential equations, describes the transmission dynamics of the disease in the human population, natural aedes aegypti mosquitoes population and wolbachia-infected mosquitoes used for control. The expression for the control reproduction number of the diseaseis derived through the next generation matrix approach. In the stability analysis, the Gershgorin’s theorem is used to obtain the condition under which the disease-free equilibrium is locally asymptotically stable. Also, in the absence of wolbachia-infected mosquitoes, the disease-free equilibrium is locally asymptotically stable if the basic offspring number and the basic reproduction  number are less than one. The presented numerical results show that the population of the  wolbachia-free aedes aegypti mosquitoes diminishes over time as compared to the population  of the wolbachia-infected mosquitoes. These results confirm that the use of wolbachia can be effective in combating the spread of yellow fever.