Vol.37, No.3, 2021, pp.331-346, doi:10.32604/csse.2021.015619
OPEN ACCESS
ARTICLE
New Fuzzy Fractional Epidemic Model Involving Death Population
• Prasantha Bharathi Dhandapani1, Dumitru Baleanu2,3,4,*, Jayakumar Thippan1, Vinoth Sivakumar1
1 Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore, 641020, India
2 Department of Mathematics, Cankaya University, Ankara, 06530, Turkey
3 Institute of Space Sciences, Magurele-Bucharest, Romania
4 Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
* Corresponding Author: Dumitru Baleanu. Email:
Received 10 November 2020; Accepted 18 December 2020; Issue published 08 March 2021
Abstract
In this research, we propose a new change in classical epidemic models by including the change in the rate of death in the overall population. The existing models like Susceptible-Infected-Recovered (SIR) and Susceptible-Infected-Recovered-Susceptible (SIRS) include the death rate as one of the parameters to estimate the change in susceptible, infected and recovered populations. Actually, because of the deficiencies in immunity, even the ordinary flu could cause death. If people’s disease resistance is strong, then serious diseases may not result in mortalities. The classical model always assumes a closed system where there is no new birth or death, no immigration or emigration, while in reality, such assumptions are not realistic. Moreover, the classical epidemic model does not report the change in population due to death caused by a disease. With this study, we try to incorporate the rate of change in the population of death caused by a disease, where the model is framed to reduce the curve of death along with the susceptible and infected populations. Since the rate of change turned out to be very small, we have tried to estimate it fractionally. Thus, the model is defined using fuzzy logic and is solved by two different methods: a Laplace Adomian decomposition method (LADM) and a differential transform method (DTM) for an arbitrary order α. To test its accuracy, we compared the results of both DTM and LADM with the fourth-order Runge-Kutta method (RKM-4) at α = 1.
Keywords
Susceptible-infected-recovered-dead; epidemic model; fractional-order; differential transformation method; Laplace Adomian decomposition method; Fourth-order; Runge-Kutta method