Mathematical modeling and control of Malaria transmission dynamics Incorporating vaccination ,Asymptomatic Carriers, Treatment, and media awareness

Abstract

Malaria remains a significant global health concern with severe socioeconomic implica tions particularly in endemic regions. A comprehensive understanding of malaria transmission dynamics is essential for designing effective control strategies, improving prevention, and sup porting eradication efforts. This dissertation develops and analyzes a set of novel, data-driven mathematical models to evaluate malaria interventions, integrating optimal control analysis and cost-effectiveness assessments. For each model, key mathematical properties such as positivity, boundedness, and the existence and stability of equilibria are established. Parameter estimation and curve fitting were performed using Ethiopian malaria incidence data, and numerical simu lations were conducted to support the analytical findings. Sensitivity analysis further identified the parameters with the greatest influence on transmission. The first model inventively examines the role of media-driven awareness in promoting insecticide utilization alongside treatment in terventions. Results conclude that combining awareness-based mosquito control with effective treatment significantly enhances the potential for malaria elimination. The second model evalu ates personal protection, expanded treatment capacity, and mosquito breeding site destruction. The findings confirm that the implementation of any single strategy, or a combination of strate gies, yields substantial impact. In addition, qualitative insights from the cost-effectiveness anal ysis suggest that integrating optimal combination of personal protective measures and mosquito breeding site destruction is the most economically efficient approach, maximizing effectiveness while optimizing resource use. The third model emphasizes the contribution of asymptomatic infections, showing that they account for nearly 30 percent of total malaria cases and play a major role in sustaining transmission. The fourth model introduces age-structured vaccination strategies within human–mosquito interactions. Both analytical and numerical results demon strate that integrating vaccination, treatment, and insecticide-based mosquito control can re duce malaria transmission to near zero, with potential for complete eradication. In conclu sion, integrating enhanced malaria treatment, awareness-based mosquito control, childhood vaccination, and effective management of asymptomatic cases can substantially reduce malaria transmission. These findings provide valuable insights for policymakers in Ethiopia and other malaria-endemic regions, informing to the design of more effective control strategies and guid ing efforts toward eventual eradication.