Mathematical modeling and analysis of COVID-19 and typhoid fever co-dynamics with treatment

A deterministic mathematical model for COVID-19 and typhoid fever co-infection was developed and analyzed to assess the effects of treatment on the transmission and control of COVID-19 and typhoid fever in the community. The model incorporates both human and pathogen populations and is subjected to analytical scrutiny, including investigations into the existence, boundedness, and positivity of the solution. The study employs the Next-Generation Matrix Method to calculate the effective reproduction number [Formula: see text], and the global stability of the disease-free equilibrium point is examined using the Lyapunov function method. Sensitivity analyses were conducted by computing Partial Rank Correlation Coefficients (PRCC) to determine the impact of each parameter on the spread or control of the diseases. The necessary conditions for the existence of optimal control and the optimality system for the model are established using Pontryagin's maximum principle. These include three control measures which are: improved COVID-19 treatment, improved typhoid fever treatment, and improved co-infection treatment. Numerical simulations of the model show that, treatment control can effectively reduce the spread of the diseases. Furthermore, increasing the treatment and screening rates can minimize the transmission of COVID-19 and typhoid fever in a population.