Analysis and simulation of a two-strain disease model with nonlinear incidence

Kuddus, Md Abdul, McBryde, Emma, Adekunle, Adeshina, and Meehan, Michael (2022) Analysis and simulation of a two-strain disease model with nonlinear incidence. Chaos, Solitons & Fractals, 155. 111637.

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Abstract

We analysed and simulated a two-strain Susceptible-Infected-Recovered (SIR) disease model with varying population size and nonlinear incidence. We found that in addition to the infection-free and two single-strain endemic equilibria, the non-linear incidence term induces a fourth equilibrium point where the two strains co-exist. We determined the conditions for the existence and stability of each of the four equilibrium points, and showed that these depend on both the traditional basic reproduction numbers () of each strain and a set of generalized threshold parameters (and ). In particular, we used appropriate Lyapunov functions to show that these generalized quantities define strict boundaries that separate regions of parameter space in which each of the equilibrium points are unstable or globally asymptotically stable. Further, we used sensitivity analysis and the Partial Rank Correlation Coefficient (PRCC) method to identify the most influential model parameters on transmission and disease prevalence, finding that the contact rate of both strains had the largest influence on both. Finally, numerical simulations were carried out to support the analytic results.

Item ID: 72745
Item Type: Article (Research - C1)
ISSN: 1873-2887
Copyright Information: © 2021 Elsevier Ltd. All rights reserved.
Date Deposited: 24 May 2022 23:11
FoR Codes: 49 MATHEMATICAL SCIENCES > 4901 Applied mathematics > 490102 Biological mathematics @ 100%
SEO Codes: 20 HEALTH > 2004 Public health (excl. specific population health) > 200404 Disease distribution and transmission (incl. surveillance and response) @ 100%
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