A sex-structured mathematical model of mosquito infection with Microsporidia MB: model reduction and release strategies

Malaria remains a significant public health burden in Sub-Saharan African countries, hindering their development. A promising strategy to combat this disease involves the use of the bacterium Microsporidia MB to reduce/replace disease-transmitting wild mosquito population. In this paper, we develop a dynamic model to analyze the transmission dynamics of Microsporidia MB within the wild mosquito population, considering both imperfect maternal and horizontal transmissions. We calculate the basic reproduction rate (R0 ) of the model to assess the invasive potential of Microsporidia MB-infected mosquito in the wild population. By establishing conditions for the local stability of equilibrium points based on the level of maternal transmission, we gain insights into the control of Microsporidia MB spread. Simplifying the model to a 2-dimensional system, we formulate and solve an optimal control problem that involves releasing infected mosquitoes to replace the wild population or achieve mosquito coexistence with sufficiently reduced wild mosquito population. Through theoretical analysis and numerical simulations, our findings contribute to the understanding and development of effective strategies for malaria control using Microsporidia MB.