COVID-19 and syphilis co-dynamic analysis using mathematical modeling approach

In this study, we have proposed and analyzed a new COVID-19 and syphilis co-infection mathematical model with 10 distinct classes of the human population (COVID-19 protected, syphilis protected, susceptible, COVID-19 infected, COVID-19 isolated with treatment, syphilis asymptomatic infected, syphilis symptomatic infected, syphilis treated, COVID-19 and syphilis co-infected, and COVID-19 and syphilis treated) that describes COVID-19 and syphilis co-dynamics. We have calculated all the disease-free and endemic equilibrium points of single infection and co-infection models. The basic reproduction numbers of COVID-19, syphilis, and COVID-19 and syphilis co-infection models were determined. The results of the model analyses show that the COVID-19 and syphilis co-infection spread is under control whenever its basic reproduction number is less than unity. Moreover, whenever the co-infection basic reproduction number is greater than unity, COVID-19 and syphilis co-infection propagates throughout the community. The numerical simulations performed by MATLAB code using the ode45 solver justified the qualitative results of the proposed model. Moreover, both the qualitative and numerical analysis findings of the study have shown that protections and treatments have fundamental effects on COVID-19 and syphilis co-dynamic disease transmission prevention and control in the community.