A qualitative analysis of a Mycoplasma genitalium epidemiological model

The objective of the article is to present a qualitative analysis of a mathematical model for the spread of a sexually transmitted infection caused by Mycoplasma genitalium. Recent investigations revealed that this pathogen is becoming resistant to the use of macrolides and can turn into a superbug in the next few years. We present an epidemiological model to describe the spread of the disease. The equilibrium points are computed, and their local and global stability are studied. In order to make the mathematical problem more realistic, we propose two different optimal control problems that establish a balance between the number of infected individuals and the use of macrolides. Several numerical illustrations regarding the solutions of the proposed problems will be provided.