Mathematical modelling of community acquired antibiotic resistant infections

Abstract

Antibiotic usage in hospitals is considered the major driver of the emergence of antibiotic resistance where selection of multiply resistant strains is most common. However, massive antibiotic consumption occurs in the community. We formulate and analyse a four state community acquired antibiotic resistance model that takes into account a forward and backward mutation. The model incorporates an extra compartment for antibiotic supply that depends on antibiotic usage. Qualitative analysis shows the existence of four possible equilibria points namely; a bacteria-free equilibrium, a bacteria sensitive only equilibrium, a bacteria resistant only equilibrium and a coexistence equilibrium. Stability analysis of the equilibrium points is performed. It is suggested that the coexistence equilibrium point can change its stability such that for a suitable chosen parameter, a limit cycle arising from Hopf bifurcation appears with an amplitude and frequency that depends on the chosen parameter. Numerical simulations are carried out based on the data for Gram-negative bacteria expressing extended-spectrum beta-lactamases which are encoded by genes derived through mutations of plasmids to illustrate theoretical results. Results suggest the need for adherence to the available best practices for antibiotic usage in order to slow down the propagation of more resistant strains.

Keywords

• Antibiotic resistance
• Sensitive strain
• Resistant strain
• Equilibrium points
• Stability analysis
• Numerical simulations