Modeling and analyzing the impact of limited medical resources and mutation on tuberculosis dynamics

Abstract

Tuberculosis (TB) remains a global health challenge despite the establishment of the End TB strategy which encouraged screening and treatment of latent patients. Existence of multiple disease strains and limited medical resources are some of the challenges hampering the success of control strategies. Hence, understanding how multiple infections and limited medical resources impact TB dynamics is of utmost importance. This study develops a novel TB model for resource limited settings that utilizes fractional order derivatives and incorporates drug-sensitive and drug-resistant strains, screening and treatment of both active patients. Drug-sensitive patients are assumed to be susceptible to infection by the drug-resistant strain (super-infection). Additionally, drug-sensitive patients have the potentila to develop drug-resistant strain due to mutation. Through mathematical analysis it has been established that the model has two reproduction numbers, which account for transmission potential of drug-sensitive and drug-resistant strain. Sensitivity analysis indicate that both reproduction numbers are largely influenced by the transmission rate. Numerical analysis suggests that when both reproduction numbers are less than unity both strain dies out. Further empirical study focused on understanding the implications of competition between the two strains showed that with time the drug-resistant strain will dominant the drug-sensitive strain. We further investigate how limited resources impact TB dynamics. The results show that limited medical resources may lead to the development and establishment of the drug-resistant cases even if the associated strain was not initially present.

Keywords

• Multidrug resistant TB
• Limited medical resources
• Fractional calculus
• Transmission dynamics