Analysis of the Effects of Rainfall and Control Measures on Chikungunya Transmission Using a Developed SEITR-SEI Model in Chad

Chikungunya is a re-emerging mosquito-borne disease whose transmission in the Sahel is strongly modulated by seasonal rainfall. In 2020, an outbreak affected the eastern provinces of Chad, yet no model to date has combined the climatic driver of the epidemic with a quantitative assessment of the available control measures. In this paper, a developed SEITR-SEI compartmental model is proposed, in which the mosquito recruitment rate is an explicit function of rainfall and a treatment class is introduced into the human population. The model is calibrated with epidemiological and entomological data from the 2020 outbreak, giving a basic reproduction number R0=4.09. We establish the positivity and boundedness of the solutions, the existence of a biologically feasible invariant region, and the local stability of the disease-free equilibrium. An optimal control problem is then formulated with three time-dependent interventions vector control, personal protection, and treatment and solved numerically using the forward–backward sweep method derived from Pontryagin's maximum principle. The results show that rainfall governs mosquito recruitment and therefore the size of the vector population, and that the three controls differ markedly in effectiveness: Personal protection alone reduces the infectious human population by 99.8% and brings the control reproduction number below unity (Rc=0.41), whereas vector control and treatment applied in isolation slow but do not reverse the epidemic (Rc=1.29 and 1.74, respectively). The combined strategy achieves near-complete containment (Rc=0.055). These findings identify personal protection as the cornerstone measure and highlight the rainy season as the critical window for intervention, providing evidence-based guidance for the control of chikungunya in Chad, and comparable climate-sensitive settings.