Modeling and Analysis of the Dynamics of Antibiotic-Susceptible and Antibiotic-Resistant Infections

Abstract

The present study, a deterministic mathematical model representing the dynamics of an infectious disease's transmission involving both drug-sensitive and drug-resistant strains is developed and analyzed. Susceptible individuals, infected with the sensitive strain, infected with the resistant strain, and recovered individuals make up the four epidemiological compartments that comprise the entire population. In order to examine how resistance development and treatment affect the spread of disease, the model is developed as a system of nonlinear ordinary differential equations. the positivity and boundedness of solutions inside a physiologically viable zone are demonstrated in order to establish model's basic qualitative characteristics. The next-generation matrix technique is used to calculate the endemic and disease-free equilibrium points as well as the fundamental reproduction number . Eigenvalue analysis is used to examine the disease-free equilibrium's local stability, and the Castillo Chavez framework is used to determine its global asymptotic stability. The study indicates that the disease will eventually be eliminated since the disease-free equilibrium is globally asymptotically stable whenever  On the other hand, a physiologically important endemic equilibrium is present when indicating continuing disease transmission within the population. Numerical simulations are used to verify the analytical results and investigate the impact of important epidemiological factors on disease dynamics, numerical simulations are carried out. The findings show that while improving the frequency of treatment successfully decreases the burden of disease, increasing the rate of resistance development and spread of the resistant strain greatly increases the occurrence of resistant infections.