RESUMEN
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.
RESUMEN
In this work, a co-infection model for human papillomavirus (HPV) and Chlamydia trachomatis with cost-effectiveness optimal control analysis is developed and analyzed. The disease-free equilibrium of the co-infection model is shown not to be globally asymptotically stable, when the associated reproduction number is less unity. It is proven that the model undergoes the phenomenon of backward bifurcation when the associated reproduction number is less than unity. It is also shown that HPV re-infection ([Formula: see text]) induced the phenomenon of backward bifurcation. Numerical simulations of the optimal control model showed that: (i) focusing on HPV intervention strategy alone (HPV prevention and screening), in the absence of C. trachomatis control, leads to a positive population level impact on the total number of individuals singly infected with C. trachomatis, (ii) Concentrating on C. trachomatis intervention controls alone (C. trachomatis prevention and treatment), in the absence of HPV intervention strategies, a positive population level impact is observed on the total number of individuals singly infected with HPV. Moreover, the strategy that combines and implements HPV and C. trachomatis prevention controls is the most cost-effective of all the control strategies in combating the co-infections of HPV and C. trachomatis.