SENSITIVITY AND OPTIMIZING DENGUE CONTROL IN A TWO-TIME-DELAY TRANSMISSION MODEL

SENSITIVITY AND OPTIMIZING DENGUE CONTROL IN A TWO-TIME-DELAY TRANSMISSION MODEL

M. Prakash Raj, A. Venkatesh, K. Arun Kumar, M. Manivel

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Abstract

This study presents a detailed analysis of a dengue transmission model that incorporates two biologically motivated time delays, representing the intrinsic and extrinsic incubation periods in host-vector interactions. Based on a vector-host framework, the model examines the influence of key transmission parameters through sensitivity analysis and contour plots. The basic reproduction number R0 is analytically derived and assessed for its dependence on epidemiologically significant factors. To curb disease spread, an optimal control problem is formulated by introducing three time-dependent control strategies: personal protection, vector control, and vector targeting efficiency. Employing Pontryagin’s Maximum Principle, the necessary conditions for optimality are established. Numerical simulations under various delay scenarios reveal that optimal control strategies significantly reduce both human and vector infections. However, the presence and magnitude of delays affect the speed and efficacy of intervention. The findings emphasize the critical role of accounting for biological delays and implementing targeted controls in designing effective dengue prevention strategies.

Keywords

Vector-Host Model, Reproduction Number, Sensitivity Analysis, Delay, Optimal Control.