Analysis and simulation of a two-strain disease model with nonlinear incidence. (February 2022)

• Record Type: Journal Article
• Authors: Kuddus, Md Abdul; McBryde, Emma S.; Adekunle, Adeshina I.; Meehan, Michael T.
• Is Part Of: Chaos, solitons and fractals. Volume 155(2022)
• Publication Date: 2022-02
• Subjects: Multi-strain -- Stability and sensitivity analysis -- Nonlinear incidence; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2021.111637
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: We investigate the dynamics of a novel two-strain disease model with nonlinear incidence We found non-linearity in the force of infection term promotes strain co-existence We derive conditions under which each of the system equilibrium points are globally asymptotically stable We find that the contact rate of each strain had the largest influence on infection prevalence 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 ( R 0 ) of each strain and a set of generalized threshold parameters ( ψ and γ ). 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.