A Fractional Model For Introducing Wolbachia Into Aedes Aegypti Mosquitoes

Abstract

In endemic areas, arboviral illnesses such as dengue and malaria continue to be a severe health burden. One strategy to reduce the number of illnesses is to substitute the major vector, Aedes aegypti, with mosquitoes that cannot transmit the virus. For this purpose, Wolbachia, an intracellular bacterium, is a good choice. Loss of Wolbachia infection, imperfect maternal transmission, lower reproductive ability, and shorter life period are all variables that impact Wolbachia dynamics in different ways in Aedes ae- gypti population. In this study, we use fractional calculus (FC) to develop a Wolbachia transmission dynamic model that accounts for imperfect maternal transmission and loss of Wolbachia infection. Wolbachia uninfected (WU) and Wolbachia infected (WI) populations are identified. The basic reproduction number (R0w|w) has been found to determine whether the Wolbachia infection is spreading or not. We have two fractional- order models: one that ignores the impact of seasons on the mosquito populations, and another that incorporates these effects. We have conducted a parametric study to identify which parameters had a significant impact on the models being analyzed. The proposed models are solved numerically with the help of the Adams-Bashforth-Moulton method. The stability of the model is analyzed using linear stability theory. Numerical test problems are studied to discuss the phenomena in detail.