Modeling and analysis of SEIRS epidemic models using homotopy perturbation method: A special outlook to 2019-nCoV in India

Abstract

Considering the prevailing situations, the mathematical modeling and dynamics of novel coronavirus (2019-nCoV) particularly in India are studied in this paper. The goal of this work is to create an effective SEIRS model to study about the epidemic. Four different SEIRS models are considered and solved in this paper using an efficient homotopy perturbation method. A clear picture of disease spreading can be obtained from the solutions derived using this method. We parametrized the model by considering the number of infection cases from 1 April 2020 to 30 June 2020. Finally, numerical analysis and graphical representations are provided to interpret the spread of virus.

Understanding COVID-19 propagation: a comprehensive mathematical model with Caputo fractional derivatives for Thailand

“…Theorem 3.2. The set of feasible solution of the system of Equation 1 with the initial conditions which initiate in R 6 + are bounded uniformly in , where…”

“…Similarly in 2022, a stuy focused on the computational dynamics of a fractional order substance addictions transfer model incorporating the Atangana-Baleanu-Caputo derivative was conducted [5]. And Thomas et al [6] delves into modeling and analyzing SEIRS epidemic models, specifically focusing on the 2019-nCoV outbreak in India, utilizing the homotopy perturbation method. In 2022, Jose et al [7] conducts stability analysis and a comparative study on various eco-epidemiological models, particularly focusing on impulsive control strategies, with a stage structure considered for both prey and predator dynamics and the study in Jose et al [8] explores the impact of strong determination and awareness on substance addictions through a mathematical modeling approach.…”

SIR Model of COVID-19 Epidemic Spread Between Two Regions

“…Abdul et al developed an SIR Model to explore the transmission dynamics of coinfection of COVID-19 and dengue and to predict the outbreak [3]. Considering those who have been exposed to the virus, Thomas Reetha et al explored four different SEIRS models and solved them with an effective homotopy perturbation method [4].Considering those who are hospitalized, Faizunnesa Khondaker et al established the SEIHR model (Susceptible (S), Exposed (E), Infected (I), Hospitalized (H), Recovered (R)) and important optimal conditions were recovered using optimal control theory to control disease transmission [5]. Considering vaccination, Kammegne Brice et al established the SEIRV model (Susceptible, Exposed, Infected, Recovered, and Vaccinated) using the reaction -diffusion equations [6].…”

Computational dynamics of a fractional order substance addictions transfer model with Atangana‐Baleanu‐Caputo derivative

“…The use of mathematical modeling is most commonly found in epidemiology, weather forecasting, human behaviors and other fields. [1][2][3][4][5][6][7] According to many studies addiction is believed to have a strong relationship with human behavior. Substance addiction (SA) has had a significant impact on the world over the last ten years.…”

“…Mathematical modeling is the act of expressing a real‐world problem in mathematical terms, usually in the form of equations and then utilizing those equations to both comprehend and uncover new aspects of the problem. The use of mathematical modeling is most commonly found in epidemiology, weather forecasting, human behaviors and other fields 1–7 . According to many studies addiction is believed to have a strong relationship with human behavior.…”