A New Numerical Scheme for Time Fractional Diffusive SEAIR Model with Non-Linear Incidence Rate: An Application to Computational Biology
Fractal and Fractional
; 6(2):78, 2022.
Article
in English
| ProQuest Central | ID: covidwho-1715225
ABSTRACT
In this paper, we propose a modified fractional diffusive SEAIR epidemic model with a nonlinear incidence rate. A constructed model of fractional partial differential equations (PDEs) is more general than the corresponding model of fractional ordinary differential equations (ODEs). The Caputo fractional derivative is considered. Linear stability analysis of the disease-free equilibrium state of the epidemic model (ODEs) is presented by employing Routh–Hurwitz stability criteria. In order to solve this model, a fractional numerical scheme is proposed. The proposed scheme can be used to find conditions for obtaining positive solutions for diffusive epidemic models. The stability of the scheme is given, and convergence conditions are found for the system of the linearized diffusive fractional epidemic model. In addition to this, the deficiencies of accuracy and consistency in the nonstandard finite difference method are also underlined by comparing the results with the standard fractional scheme and the MATLAB built-in solver pdepe. The proposed scheme shows an advantage over the fractional nonstandard finite difference method in terms of accuracy. In addition, numerical results are supplied to evaluate the proposed scheme’s performance.
Mathematics; proposed fractional scheme; diffusive epidemic model; non-linear incidence rate; stability; convergence; Infections; Infectious diseases; Accuracy; Calculus; Pathogens; Investigations; Severe acute respiratory syndrome coronavirus 2; Epidemiology; Asymptomatic; Finite difference method; Equilibrium; Epidemics; Stability criteria; Partial differential equations; Viruses; Stability analysis; Mathematical models; Disease prevention; Coronaviruses; Disease transmission; COVID-19; China
Full text:
Available
Collection:
Databases of international organizations
Database:
ProQuest Central
Type of study:
Observational study
Language:
English
Journal:
Fractal and Fractional
Year:
2022
Document Type:
Article
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