Introduction: Microsporidia MB are naturally occurring, vertically and horizontally transmitted symbionts of mosquitoes that can influence reproductive outcomes. Understanding their invasion dynamics is essential for clarifying their ecological role and interaction with conventional vector control strategies. This study presents a mathematical framework to examine the establishment and persistence of microsporidia MB in a mosquito population exposed to chemical interventions.
Methods: We formulate and analyse a deterministic compartmental model structured by infection status, sex (male and female), and developmental stage (eggs, larvae, and adults). The model incorporates vertical transmission, horizontal transmission through mating, and reduced egg viability associated with specific mating combinations. Larval and adult control measures are represented through compliance and efficacy parameters that increase stage-specific mortality. The basic reproduction number is derived using the next-generation matrix method. Local stability is determined via eigenvalue analysis of the Jacobian matrix, while global stability is established using a quadratic Lyapunov function. Numerical simulations explore the influence of key biological and control parameters on infection prevalence and overall population dynamics.
Results: The analysis establishes threshold conditions governing invasion and persistence. The infection-free, complete-infection, and coexistence equilibria are shown to be locally stable under appropriate reproduction number conditions. Vertical transmission efficiency and egg viability parameters are critical for long-term persistence, whereas horizontal transmission accelerates spread after introduction. Chemical control significantly affects both infection prevalence and mosquito abundance, with outcomes depending on coverage and efficacy levels.
Conclusions: The model provides a mechanistic basis for understanding microsporidia invasion in structured mosquito populations and offers quantitative insight into their interaction with chemical control within integrated vector management.
