An optimal control model for COVID‐19, zika, dengue, and chikungunya co‐dynamics with reinfection

The co‐circulation of different emerging viral diseases is a big challenge from an epidemiological point of view. The similarity of symptoms, cases of virus co‐infection, and cross‐reaction can mislead in the diagnosis of the disease. In this article, a new mathematical model for COVID‐19, zika, chikungunya, and dengue co‐dynamics is developed and studied to assess the impact of COVID‐19 on zika, dengue, and chikungunya dynamics and vice‐versa. The local and global stability analyses are carried out. The model is shown to undergo a backward bifurcation under a certain condition. Global sensitivity analysis is also performed on the parameters of the model to determine the most dominant parameters. If the zika‐related reproduction number ℛ0Z$$ {\mathcal{R}}_{0\mathrm{Z}} $$ is used as the response function, then important parameters are: the effective contact rate for vector‐to‐human transmission of zika (β2h$$ {\beta}_2^h $$, which is positively correlated), the human natural death rate (ϑh$$ {\vartheta}^h $$, positively correlated), and the vector recruitment rate (Ψv$$ {\Psi}^v $$, also positively correlated). In addition, using the class of individuals co‐infected with COVID‐19 and zika (ℐCZh$$ {\mathcal{I}}_{\mathrm{CZ}}^h $$) as response function, the most dominant parameters are: the effective contact rate for COVID‐19 transmission (β1$$ {\beta}_1 $$, positively correlated), the effective contact rate for vector‐to‐human transmission of zika (β2h$$ {\beta}_2^h $$, positively correlated). To control the co‐circulation of all the diseases adequately under an endemic setting, time dependent controls in the form of COVID‐19, zika, dengue, and chikungunya preventions are incorporated into the model and analyzed using the Pontryagin's principle. The model is fitted to real COVID‐19, zika, dengue, and chikungunya datasets for Espirito Santo (a city with the co‐circulation of all the diseases), in Brazil and projections made for the cumulative cases of each of the diseases. Through simulations, it is shown that COVID‐19 prevention could greatly reduce the burden of co‐infections with zika, dengue, and chikungunya. The negative impact of the COVID‐19 pandemic on the control of the arbovirus diseases is also highlighted. Furthermore, it is observed that prevention controls for zika, dengue, and chikungunya can significantly reduce the burden of co‐infections with COVID‐19.