A Sex-Structured Mmathematical Model of Mosquito Infection with Microsporidia MB: Model Reduction and Release Strategies
摘要
Malaria remains a significant public health burden in Sub-Saharan African countries, hindering their development. With no effective vaccine currently available, controlling the malaria vector population remains the most effective preventive measure. 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. In this paper, we develop a dynamic mathematical model to analyze the transmission dynamics of Microsporidia MB within wild mosquito populations, accounting for both imperfect maternal and horizontal transmission. We derive and analyze a threshold condition to assess the potential for Microsporidia MB-infected mosquitoes to invade and persist in the wild population. By establishing conditions for the local stability of equilibrium points, we explore the influence of maternal transmission on the spread of Microsporidia MB. Additionally, we employ a cascade reduction approach to simplify the model into a two-dimensional system and formulate an optimal control problem. Using Pontryagin’s Maximum Principle, we determine optimal release strategies for infected mosquitoes to either replace the wild population or promote coexistence with a significantly 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.