Numerical analysis of diffusive susceptible-infected-recovered epidemic model in three space dimension. (March 2020)

• Record Type: Journal Article
• Authors: Ahmed, Nauman; Ali, Mubasher; Baleanu, Dumitru; Rafiq, Muhammad; Rehman, Muhammad Aziz ur
• Is Part Of: Chaos, solitons and fractals. Volume 132(2020)
• Publication Date: 2020-03
• Subjects: Operator splitting methods -- Nonstandard finite difference schemes -- Positivity -- SIR epidemic model -- Numerical stability -- Bifurcation value; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2019.109535
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: Three dimensional reaction-diffusion epidemic system is considered for numerical study. Numerical stability of the epidemic system and bifurcation value of transmission parameter from susceptibility to disease is evaluated with the help of Routh–Huwartiz criteria. A novel structure preserving numerical method is proposed for solution of reaction-diffusion epidemic model in three dimension. Simulations of a numerical experiment are presented to verify all the attributes of the proposed method. Abstract: In this article, numerical solution of three dimensional susceptible-infected-recovered (SIR) reaction-diffusion epidemic system is furnished with a time efficient operator splitting nonstandard finite difference (OS-NSFD) method. We perform the comparison of proposed OS-NSFD method with popular forward Euler explicit finite difference (FD) method and time efficient backward Euler operator splitting finite difference (OS-FD) implicit method. The proposed OS-NSFD method is implicit in nature but computationally efficient as compared to forward Euler explicit (FD) scheme. The numerical stability and bifurcation value of transmission coefficient for SIR reaction-diffusion epidemic system is also investigated with the aid of Routh–Hurwitz method. At the end, we give two numerical experiments and simulation. In first experiment, all the numerical schemes are compared with the help of simulations. In second experiment we show the simulations of proposed NSFD technique at different values of parameters. Also we discuss the importance of transmission rate to control the spread of disease with the help of simulations.