Caputo fractional reduced differential transform method for SEIR epidemic model with fractional order

2021 ◽  
Vol 8 (3) ◽  
pp. 537-548
Author(s):  
S. E. Fadugba ◽  
◽  
F. Ali ◽  
A. B. Abubakar ◽  
◽  
...  
Keyword(s):  
Power Series ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Epidemic Model ◽  
Differential Transform Method ◽  
Host Community ◽  
Convergent Power Series ◽  
Transform Method ◽  
Differential Transform ◽  
Reduced Differential Transform Method

This paper proposes the Caputo Fractional Reduced Differential Transform Method (CFRDTM) for Susceptible-Exposed-Infected-Recovered (SEIR) epidemic model with fractional order in a host community. CFRDTM is the combination of the Caputo Fractional Derivative (CFD) and the well-known Reduced Differential Transform Method (RDTM). CFRDTM demonstrates feasible progress and efficiency of operation. The properties of the model were analyzed and investigated. The fractional SEIR epidemic model has been solved via CFRDTM successfully. Hence, CFRDTM provides the solutions of the model in the form of a convergent power series with easily computable components without any restrictive assumptions.

scholarly journals NUMERICAL SOLUTION FOR TIME-FRACTIONAL MURRAY REACTION-DIFFUSION EQUATIONS VIA REDUCED DIFFERENTIAL TRANSFORM METHOD

2021 ◽  
Author(s):  
Muhammed Yiğider ◽  
Serkan Okur
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Differential Transform Method ◽  
Reaction Diffusion Equations ◽  
Transform Method ◽  
Differential Transform ◽  
Fractional Differential ◽  
Reduced Differential Transform Method ◽  
Time Fractional Differential Equations

In this study, solutions of time-fractional differential equations that emerge from science and engineering have been investigated by employing reduced differential transform method. Initially, the definition of the derivatives with fractional order and their important features are given. Afterwards, by employing the Caputo derivative, reduced differential transform method has been introduced. Finally, the numerical solutions of the fractional order Murray equation have been obtained by utilizing reduced differential transform method and results have been compared through graphs and tables. Keywords: Time-fractional differential equations, Reduced differential transform methods, Murray equations, Caputo fractional derivative.

scholarly journals Epidemic Model of Leptospirosis Containing Fractional Order

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Muhammad Altaf Khan ◽  
S. F. Saddiq ◽  
Saeed Islam ◽  
Ilyas Khan ◽  
Dennis Ling Chuan Ching
Keyword(s):  
Approximate Solution ◽  
Positive Solution ◽  
Fractional Order ◽  
Epidemic Model ◽  
Differential Transform Method ◽  
Unique Positive Solution ◽  
Transform Method ◽  
Differential Transform ◽  
Generalized Differential ◽  
Order Four

We study an epidemic model of leptospirosis in fractional order numerically. The multistep generalized differential transform method is applied to find the accurate approximate solution of the epidemic model of leptospirosis disease in fractional order. A unique positive solution for the epidemic model in fractional order is presented. For the integer case derivative, the approximate solution of MGDTM is compared with the Runge-Kutta order four scheme. The numerical results are presented for the justification purpose.

ROLE OF REINFECTION IN TRANSMISSION DYNAMICS OF COVID-19: A SEMI-ANALYTICAL APPROACH USING DIFFERENTIAL TRANSFORM METHOD

2021 ◽  
Vol 6 (1) ◽  
pp. 745
Author(s):  
Opeyemi Odetunde ◽  
Jibril Lawal ◽  
Ally Yeketi Ayinla
Keyword(s):  
Treatment Strategies ◽  
Differential Transform Method ◽  
Host Community ◽  
Transmission Dynamics ◽  
Transform Method ◽  
Social Distancing ◽  
Linear System Of Equations ◽  
Differential Transform ◽  
Non Linear System

Reinfection of a recovered individual either as a result of relapse or new contact no doubt poses a major threat to the eradication of an infection within the host community. In this work, the role of re-infection in the transmission dynamics of COVID-19 was considered and analysed using the semi-analytical tool Differential Transform Method (DTM). COVID-19 (also known as Coronavirus) has shut down the economy of the world since it became a global pandemic. A mathematical model was constructed with consideration of multiple pathways of infection transmission, the treatment strategies and policies adopted (social distancing, wearing of face mask and so on) to limit the spread of the infection globally. The non-linear system of equations governing the model was solved using DTM and the resulting series solution was compared with the standard numeric Runge-Kutta order 4 (RK4). It was discovered that re-integration of a recovered individual into the susceptible community without observing the prevention guidelines such as social distancing, washing of hands and proper sanitizing could increase the spread of the infection since the recovered individuals are not guaranteed of immunity against the infection after recovery. The study concluded that families of recovered patients must ensure adequate preventive measure while integrating their recovered loved ones back to their midst.

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