Mathematical analysis of a two-strain disease model with amplification. (February 2021)

• Record Type: Journal Article
• Authors: Kuddus, Md Abdul; McBryde, Emma S.; Adekunle, Adeshina I.; White, Lisa J.; Meehan, Michael T.
• Is Part Of: Chaos, solitons and fractals. Volume 143(2021)
• Publication Date: 2021-02
• Subjects: drug resistance -- multi-strain -- stability analysis; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2020.110594
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: Our two-strain disease model with amplification of drug resistance shows that the resistant strain can drive out the drug-susceptible strain but not the reverse. Even with a fitness cost, drug resistant strains may have higher prevalence than drug susceptible strains. Poor quality treatment promotes strain coexistence. Abstract: We investigate a two-strain disease model with amplification to simulate the prevalence of drug-susceptible (s) and drug-resistant (m) disease strains. Drug resistance first emerges when drug-susceptible strains mutate and become drug-resistant, possibly as a consequence of inadequate treatment, i.e. amplification. In this case, the drug-susceptible and drug-resistant strains are coupled. We perform a dynamical analysis of the resulting system and find that the model contains three equilibrium points: a disease-free equilibrium; a mono-existent disease-endemic equilibrium at which only the drug-resistant strain persists; and a co-existent disease-endemic equilibrium where both the drug-susceptible and drug-resistant strains persist. We found two basic reproduction numbers: one associated with the drug-susceptible strain ( R 0 s ) ; the other with the drug-resistant strain ( R 0 m ), and showed that at least one of the strains can spread in a population if max [ R 0 s, R 0 m ] > 1 . Furthermore, we also showed that if R 0 m > max [ R 0 s, 1 ], the drug-susceptible strain dies out but the drug-resistant strain persists in the population (mono-existent equilibrium); however if R 0 s > max [ R 0 m, 1 ], then both the drug-susceptible and drug-resistant strains persist in the population (co-existent equilibrium). We conducted a local stability analysis of the system equilibrium points using the Routh-Hurwitz conditions and a global stability analysis using appropriate Lyapunov functions. Sensitivity analysis was used to identify the key model parameters that drive transmission through calculation of the partial rank correlation coefficients (PRCCs). We found that the contact rate of both strains had the largest influence on prevalence. We also investigated the impact of amplification and treatment/recovery rates of both strains on the equilibrium prevalence of infection; results suggest that poor quality treatment/recovery makes coexistence more likely and increases the relative abundance of resistant infections.