Optimal Control Analysis and Cost – Effectiveness of Dengue Transmission Model Along With Implementation Time Effects in Applying the Control Interventions

Abstract

Dengue fever poses a significant global public health threat, and its effective management requires a comprehensive approach to control the dengue prevalence. This study proposes an optimal control problem for the dengue transmission, incorporating three key control measures: information‐induced self‐protection, saturated treatment, and pesticide use for vector control, and is analyzed using Pontryagin's Maximum Principle. Importantly, a novel higher nonlinearity in the cost construction is incorporated. Seven distinct control policies ( P1−P7$$ {P}_1-{P}_7 $$ ) incorporating different combinations of control measures are designed and evaluated through numerical simulations. The results demonstrate that the combined strategy of all controls (Policy P7$$ {P}_7 $$ ) is the most effective, reducing infection prevalence to minimal levels within approximately 60 days, while maintaining sustained control thereafter. In comparison, the combined use of information and treatment (Policy P4$$ {P}_4 $$ ) achieves a similar outcome but requires nearly 120 days to stabilize the infection. Among single‐control strategies, information‐induced self‐protection (Policy P1$$ {P}_1 $$ ) outperforms treatment ( P2$$ {P}_2 $$ ) and pesticide application ( P3$$ {P}_3 $$ ) when applied alone. Cost‐effectiveness analysis using CCER, IAR, and ICER reveals that Policy P1$$ {P}_1 $$ is the most cost‐effective intervention, with the lowest CCER value, while Policy P7$$ {P}_7 $$ averts the highest number of infections. Furthermore, the analysis shows that the control's effectiveness depends strongly on epidemic severity: for mild outbreaks ( R0≤2.5$$ {R}_0\le 2.5 $$ ), combined strategies such as P4$$ {P}_4 $$ and P6$$ {P}_6 $$ (treatment and pesticide) perform efficiently, whereas for severe outbreaks ( R0>2.5$$ {R}_0>2.5 $$ ), comprehensive control ( P7$$ {P}_7 $$ ) becomes essential. Additionally, delayed implementation of control measures significantly worsens disease outcomes, increasing infection peaks and economic burden. Overall, the study highlights the importance of timely and integrated intervention strategies and provides quantitative insights for optimal resource allocation in dengue control.