Eur. Phys. J. Plus (2021) 136: 1090
https://doi.org/10.1140/epjp/s13360-021-02030-6

Regular Article

COVID-19 and dengue co-infection in Brazil: optimal control and cost-effectiveness analysis

¹ Department of Mathematics, Federal University of Technology, Owerri, Nigeria
² Mathematics Department, University of Dar es Salaam, P.O. Box 35062, Dar es Salaam, Tanzania
³ Departement de Mathematiques, UFR des Sciences et Technologies, Universite de Thies, Thies, Senegal
⁴ School of Computer Science and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa
⁵ School of Computational and Communication Sciences and Engineering, Nelson Mandela African Institution of Science and Technology, P.O. Box 447, Arusha, Tanzania

^a andrew.omame@futo.edu.ng, omame2020@gmail.com

Received: 18 August 2021
Accepted: 2 October 2021
Published online: 29 October 2021

Abstract

A mathematical model for the co-interaction of COVID-19 and dengue transmission dynamics is formulated and analyzed. The sub-models are shown to be locally asymptotically stable when the respective reproduction numbers are below unity. Using available data sets, the model is fitted to the cumulative confirmed daily COVID-19 cases and deaths for Brazil (a country with high co-endemicity of both diseases) from February 1, 2021 to September 20, 2021. The fitting was done using the fmincon function in the Optimization Toolbox of MATLAB. Parameters denoting the COVID-19 contact rate, death rate and loss of infection acquired immunity to COVID-19 were estimated using the two data sets. The model is then extended to include optimal control strategies. The appropriate conditions for the existence of optimal control and the optimality system for the co-infection model are established using the Pontryagin’s Principle. Different control strategies and their cost-effectiveness analyses were considered and simulated for the model, which include: controls against incident dengue and COVID-19 infections, control against co-infection with a second disease and treatment controls for both dengue and COVID-19. Highlights of the simulation results show that: (1) dengue prevention strategy could avert as much as 870,000 new COVID-19 infections; (2) dengue only control strategy or COVID-19 only control strategy significantly reduces new co-infection cases; (3) the strategy implementing control against incident dengue infection is the most cost-effective in controlling dengue and COVID-19 co-infections.