Non-standard discretizations of SIS epidemiological model with or without diffusion
| dc.contributor.author | Lubuma, Jean | |
| dc.contributor.author | Mureithi, Eunice | |
| dc.contributor.author | Terefe, Yibeltal | |
| dc.date.accessioned | 2018-11-08T10:19:44Z | |
| dc.date.available | 2018-11-08T10:19:44Z | |
| dc.date.issued | 2014 | |
| dc.description.abstract | We design and investigate the reliability of various nonstandard finite difference (NSFD) schemes for SIS-type epidemiological models. The success of the study is due to an innovative use of Mickens’ rules of complex denominator functions and nonlocal approximation of nonlinear terms. For the classical SIS-ODE model, we construct for the first time a nonstandard Runge- Kutta method, which is shown to be of order four. We also consider two new NSFD schemes which faithfully replicate the property of the continuous model of having the value R0 = 1 of the basic reproduction parameter as a forward bifurcation: the disease-free equilibrium is globally asymptotically stable when R0 < 1; it is unstable when R0 > 1 and there appears a unique locally asymptotically stable endemic equilibrium in this case. The latter schemes are further used to derive NSFD schemes that are dynamically consistent with the positivity and boundedness properties of the SIS-diffusion model for the spatial spread of disease. Numerical simulations that support the theory are provided. | en_US |
| dc.identifier.doi | 10.1090/conm/618/12326 | |
| dc.identifier.uri | http://hdl.handle.net/20.500.11810/4984 | |
| dc.language.iso | en | en_US |
| dc.publisher | Contemporary Mathematics, Mathematics of Continuous and Discrete Dynamical System | en_US |
| dc.title | Non-standard discretizations of SIS epidemiological model with or without diffusion | en_US |
| dc.type | Journal Article, Peer Reviewed | en_US |
| dc.type | Journal Article, PrePrint | en_US |