Mathematical Modeling of the Effects of Optimized Drainage Systems on Mosquito Dynamics in Prevention of Malaria

Resumo

Malaria continues to pose a major public health threat especially in tropical regions like Nigeria where inadequate drainage systems create stagnant water that fosters mosquito breeding. While conventional interventions such as insecticide-treated nets, indoor spraying, and antimalarial drugs remain essential, environmental management has been comparatively underexplored. This study presents a six-compartment mathematical model that incorporates human and mosquito population dynamics alongside open and closed drainage systems to evaluate their role in controlling malaria transmission. The model integrates susceptible, infected, and recovered classes in both populations and introduces drainage effectiveness parameters (κO and κC) to simulate the reduction in mosquito habitats. Analytical findings show that when κO + κC > 1, the disease-free equilibrium becomes locally asymptotically stable which effectively halting endemic transmission. The basic reproduction number (R0) is derived and results confirm that optimized drainage can bring R0 below the critical threshold of 1 which is a necessary condition for disease elimination. An optimization framework using Lagrangian techniques further demonstrates that an equal allocation of drainage resources (κODO = κCDC = c/2) yields the most efficient reduction in mosquito populations. Sensitivity analyses highlight that higher mosquito reproduction (ρm) and contact rates (β2) exacerbate disease persistence there by reinforcing the need for an integrative approaches. This study underscores the potential of drainage optimization as a sustainable, evidence-based addition to malaria control strategies. It offers actionable recommendations for policymakers to integrate environmental management into public health frameworks aimed at achieving malaria elimination by 2030.