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 Script capital 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 (beta 2h$$ {\beta}_2<^>h $$, which is positively correlated), the human natural death rate (& thetasym;h$$ {\vartheta}<^>h $$, positively correlated), and the vector recruitment rate (psi v$$ {\Psi}<^>v $$, 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 (beta 1$$ {\beta}_1 $$, positively correlated), the effective contact rate for vector-to-human transmission of zika (beta 2h$$ {\beta}_2<^>h $$, 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.