A Generalized Mathematical Model of Hard-to-treat Infections with Culturing and Antibiotic Susceptibility Testing

Abstract

A mathematical model for hard-to-treat infections with culturing and antibiotic susceptibility testing (CAST) as an intervention strategy in a population is formulated and analysed. The analysis of the model has been done qualitatively to investigate the existence and stability of equilibria. Using the Lyapunov function, the disease-free equilibrium of the model proved to be globally asymptotically stable with respect to the threshold quantity R_c<1. Of course, this entails local stability. A similar approach is employed in proving the global stability of the endemic equilibrium state in the case R_c>1. However, the local stability of the endemic equilibrium is investigated using the method of row elimination. The model was validated using the Tuberculosis case in South Africa, and the result reveals that patients without adopting CAST strategy are prone to drug resistance and delay in quick response to the treatment regimen. On the contrary, individuals who have adopted the strategy have shown greater recovery potential from the infection. Based on that, self - medication, blind prescription should be avoided to curtail the consequences of drug resistance.

Keywords

• Hard-to-treat infections
• Antibiotics susceptibility testing
• Global stability
• Culturing
• Lyapunov function

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