Optimal control strategies for the transmission dynamics of Giardiasis

Сажетак

This work develops and examines a deterministic mathematical model of giardiasis transmission, explicitly including the frequently neglected influence of asymptomatic carriers and the environmental pathogen reservoir. A thorough dynamical systems analysis of the autonomous model is performed, confirming the positivity and boundedness of solutions to ensure epidemiological well-posedness. We calculate the basic reproduction number (R0) employing the next-generation matrix approach and formally delineate the criteria for the local asymptotic stability of the disease-free equilibrium. We enhance the model by incorporating optimum control theory to meet the essential requirement for economical, time-sensitive intervention tactics. We provide three dynamic control functions that represent the medical treatment of symptomatic persons, the active
screening of asymptomatic carriers, and environmental sanitation initiatives. Utilizing Pontryagin’s Maximum Principle, we establish the requisite conditions for optimal control and simulate diverse intervention scenarios. Our findings demonstrate that single-intervention methods achieve limited efficacy, but a multifaceted, integrated strategy substantially reduces both the human disease burden and environmental pollution. Moreover, we illustrate that a focused strategy integrating immediate treatment with proactive asymptomatic screening provides a highly cost-effective option for resource-limited environments. This study offers substantial mathematical insights and a quantitative public health framework for the development of effective and sustainable giardiasis control initiatives.