Optimal control and cost-effectiveness analysis of nonlinear deterministic Zika virus model

The Zika Virus epidemic (ZIKV) became an emergency and a public health concern as it hampered the growth and wellness of French Polynesia, Central America, Brazil, Yap Island, and the Caribbean during the 2015–2016 infective period. The disease is transmitted to the human host through the bite of an Aedes species of mosquitoes and has been a threat to humans. The research considers a non-linear ZIKV model, capturing the aquatic compartment of the vector. The preliminary analysis of the non-negative and well-posedness of the ZIKV model is determined. Further, the ZIKV-free and endemic equilibria of the model are determined, and their comprehensive local and global stability analyses are established. The analysis results showed that the ZIKV model exhibits forward bifurcation at the point \(D_{E_0}\) $D_{E_0}$ , which means that bringing the \({\mathcal {R}}_{0}\) ${\mathcal{R}}_0$ to be less than 1 is sufficient to mitigate the disease. The model was restructured into an intervention model to identify the strategy that will halt the ZIKV transmission. Lastly, to estimate the cost associated with executing the strategies, a cost-effective analysis was carried out to determine the strategy that gives the best reward with the least monetary input. The analysis showed that strategy H is the most cost-effective strategy among the outlined strategies. From the analysis, we recommend that vaccines and vaccination programs be integrated into the intervention measures for controlling ZIKV disease since they have an uncompromising impact on mitigating the disease when combined with the other known measures.