Mathematical analysis of a two-strain disease model with amplification

We investigate a two-strain disease model with amplification to simulate the prevalence of drug-susceptible (s) and drug-resistant (m) strains. Drug resistance first emerges when strains mutate become drug-resistant, possibly as consequence inadequate treatment, i.e. amplification. In this case, are coupled. perform dynamical analysis resulting system find that contains three equilibrium points: disease-free equilibrium; mono-existent disease-endemic at which only strain persists; co-existent where both persist. found two basic reproduction numbers: one associated (R0s); other (R0m), showed least can spread in population if max[R0s,R0m]>1. Furthermore, we also R0m>max[R0s,1], dies out but persists (mono-existent equilibrium); however R0s>max[R0m,1], then persist (co-existent equilibrium). conducted local stability points using Routh-Hurwitz conditions global appropriate Lyapunov functions. Sensitivity was used identify key parameters drive transmission through calculation partial rank correlation coefficients (PRCCs). contact rate had largest influence on prevalence. investigated impact treatment/recovery rates infection; results suggest poor quality makes coexistence more likely increases relative abundance resistant infections.