Mathematical analysis of a two-strain disease model with amplification

Kuddus, Md Abdul, McBryde, Emma S., Adekunle, Adeshina I., White, Lisa J., and Meehan, Michael T. (2021) Mathematical analysis of a two-strain disease model with amplification. Chaos Solitons and Fractals, 143. 110594.

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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 ; the other with the drug-resistant strain and showed that at least one of the strains can spread in a population if . Furthermore, we also showed that if , the drug-susceptible strain dies out but the drug-resistant strain persists in the population (mono-existent equilibrium); however if , 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.

Item ID: 65435
Item Type: Article (Research - C1)
ISSN: 1873-2887
Keywords: Drug resistance, Multi-strain, Stability analysis
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Copyright Information: © 2020 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (
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A version of this publication was included as Chapter 4 of the following PhD thesis: Kuddus, Md Abdul (2021) Using mathematical models to develop tuberculosis control strategies in Bangladesh. PhD thesis, James Cook University, which is available Open Access in ResearchOnline@JCU. Please see the Related URLs for access.

Funders: James Cook University (JCU)
Projects and Grants: JCU-QLD-835481
Date Deposited: 08 Jan 2021 00:10
FoR Codes: 49 MATHEMATICAL SCIENCES > 4901 Applied mathematics > 490105 Dynamical systems in applications @ 50%
42 HEALTH SCIENCES > 4202 Epidemiology > 420205 Epidemiological modelling @ 50%
SEO Codes: 97 EXPANDING KNOWLEDGE > 970101 Expanding Knowledge in the Mathematical Sciences @ 30%
92 HEALTH > 9204 Public Health (excl. Specific Population Health) > 920404 Disease Distribution and Transmission (incl. Surveillance and Response) @ 70%
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