Fractional order bacterial infection model with effects of anti-virulence drug and antibiotic

Abstract

A model examining the population dynamics of susceptible bacteria, resistant bacteria, adaptive immunity cells and innate cells in an infected individual receiving multiple antibiotics and antivirulence drug is proposed by a fractional-order differential equations in Caputo sense. The existence and uniqueness of the solutions the model as well as their non-negativity and boundedness have been discussed. The reproduction numbers of the proposed model through the next generation matrix procedure are developed. The existence and stability of the equilibrium points were shown. To demonstrate the model's ability to be applicable on a real-world example, the numerical simulations were carried out by using parameter values acquired from the literature for Mycobacterium Tuberculosis (Mtb) and Pseudomonas Aeruginosa (Pa). The effects of antivirulence drug therapy in addition to antibiotic therapy have been also investigated. The role of antivirulence drug therapy in eliminating infectious bacteria was discussed in the simulations obtained in accordance with the recommended treatment processes for these bacteria. In addition, the model was simplified by considering the situation in which no drug treatment was administered, and its analysis was also carried out. Sensitivity analysis of the reproduction numbers was performed in the light of the values used in simulations.