Modeling the co-dynamics of vector-borne infections with the application of optimal control theory

The pathogens of dengue and chikungunya are transmitted by Aedes aegypti mosquitoes, presenting a significant likelihood of vectors and hosts being concurrently infected by both viruses. We present biological insights into the co-infection of chikungunya and dengue to elucidate the phenomena clearly. Therefore, we develop a mathematical model to conceptualize the intricate dynamics of chikungunya and dengue co-infection. We investigate the models of dengue fever and chikungunya separately, examining their local and global asymptotic stability. It has been shown that these models have a unique endemic steady state. Moreover, we demonstrate that both diseases are uniformly persistent when the reproduction parameter exceeds one. The endemic indicator, which is the reproduction value of the co-infected model, is computed as the maximum of the reproduction values of dengue and chikungunya. Moreover, the theory of optimal control is implemented using four distinct strategies to reduce infection levels: prevention through insect repellents, control via vaccination, and vector reduction through larvicides and adulticides. Finally, we investigate the system numerically to illustrate the overall dynamics of co-infection under optimal control measures and to assess the effectiveness of these control policies.