scholarly journals Abundant stable novel solutions of fractional-order epidemic model along with saturated treatment and disease transmission

Open Physics ◽  
2021 ◽  
Vol 19 (1) ◽  
pp. 843-852
Author(s):  
Mostafa M. A. Khater ◽  
Dianchen Lu ◽  
Samir A. Salama
Keyword(s):  
Fractional Order ◽  
Epidemic Model ◽  
Disease Transmission ◽  
Analytical Techniques ◽  
Expansion Method ◽  
Sis Epidemic Model ◽  
Modified Kudryashov Method ◽  
Simplest Equation Method ◽  
Kudryashov Method ◽  
Saturated Treatment

Abstract This article proposes and analyzes a fractional-order susceptible, infectious, susceptible (SIS) epidemic model with saturated treatment and disease transmission by employing four recent analytical techniques along with a novel fractional operator. This model is computationally handled by extended simplest equation method, sech–tanh expansion method, modified Khater method, and modified Kudryashov method. The results’ stable characterization is investigated through the Hamiltonian system’s properties. The analytical solutions are demonstrated through several numerical simulations.

Analysis of a fractional-order SIS epidemic model with saturated treatment

2020 ◽  
pp. 2150004
Author(s):  
Soovoojeet Jana ◽  
Manotosh Mandal ◽  
Swapan Kumar Nandi ◽  
T. K. Kar
Keyword(s):  
Hopf Bifurcation ◽  
Global Stability ◽  
Fractional Order ◽  
Epidemic Model ◽  
Disease Transmission ◽  
Equilibrium Points ◽  
Sis Epidemic Model ◽  
Proposed Model ◽  
Saturated Treatment ◽  
Sis Epidemic

In this paper, we propose and analyze a fractional-order SIS epidemic model with the saturated treatment and disease transmission. The existence and uniqueness, nonnegativity and finiteness of solutions for our suggested model have been studied. Different equilibria of the model are found and their local and global stability analyses are also examined. Furthermore, the conditions for fractional backward and fractional Hopf bifurcation are also analyzed in both the commensurate and incommensurate fractional-order model. We study how the control parameter and the order of the fractional derivative play role in local as well as global stability of equilibrium points and Hopf bifurcation. We have demonstrated the analytical results of our proposed model system through several numerical simulations.

Analysis of a fuzzy epidemic model with saturated treatment and disease transmission

2018 ◽  
Vol 11 (01) ◽  
pp. 1850002 ◽  
Author(s):  
Swapan Kumar Nandi ◽  
Soovoojeet Jana ◽  
Manotosh Manadal ◽  
T. K. Kar
Keyword(s):  
Epidemic Model ◽  
Disease Transmission ◽  
Fuzzy Numbers ◽  
Transmission Rate ◽  
Dynamical Behavior ◽  
Threshold Condition ◽  
Sis Epidemic Model ◽  
Fuzzy Expected Value ◽  
Treatment Function ◽  
Saturated Treatment

In this paper, we describe an SIS epidemic model where both the disease transmission rate and treatment function are considered in saturated forms. The dynamical behavior of the system is analyzed. The system is customized by considering the disease transmission rate and treatment control as fuzzy numbers and then fuzzy expected value of the infected individuals is determined. The fuzzy basic reproduction number is investigated and a threshold condition of pathogen is derived at which the system undergoes a backward bifurcation.

scholarly journals Global dynamics and bifurcation analysis of a fractional-order SEIR epidemic model with saturation incidence rate

2021 ◽  
Author(s):  
Parvaiz Ahmad Naik ◽  
Muhammad Bilal Ghori ◽  
Jian Zu ◽  
Zohre Eskandari ◽  
Mehraj-ud-din Naik
Keyword(s):  
Incidence Rate ◽  
Fractional Order ◽  
Epidemic Model ◽  
Disease Transmission ◽  
Disease Status ◽  
Host Population ◽  
Sensitivity Analyses ◽  
Feasible Region ◽  
Global Dynamics ◽  
Globally Stable

The present paper studies a fractional-order SEIR epidemic model for the transmission dynamics of infectious diseases such as HIV and HBV that spreads in the host population. The total host population is considered bounded, and Holling type-II saturation incidence rate is involved as the infection term. Using the proposed SEIR epidemic model, the threshold quantity, namely basic reproduction number R0, is obtained that determines the status of the disease, whether it dies out or persists in the whole population. The model’s analysis shows that two equilibria exist, namely, disease-free equilibrium (DFE) and endemic equilibrium (EE). The global stability of the equilibria is determined using a Lyapunov functional approach. The disease status can be verified based on obtained threshold quantity R0. If R0 < 1, then DFE is globally stable, leading to eradicating the population’s disease. If R0 > 1, a unique EE exists, and that is globally stable under certain conditions in the feasible region. The Caputo type fractional derivative is taken as the fractional operator. The bifurcation and sensitivity analyses are also performed for the proposed model that determines the relative importance of the parameters into disease transmission. The numerical solution of the model is obtained by the generalized Adams- Bashforth-Moulton method. Finally, numerical simulations are performed to illustrate and verify the analytical results.

scholarly journals On the solution of fractional order SIS epidemic model

2018 ◽  
Vol 117 ◽  
pp. 168-174 ◽  
Author(s):  
M. Hassouna ◽  
A. Ouhadan ◽  
E.H. El Kinani
Keyword(s):  
Fractional Order ◽  
Epidemic Model ◽  
Sis Epidemic Model ◽  
Sis Epidemic

New optical soliton solutions for Fokas–Lenells dynamical equation via two various methods

2021 ◽  
pp. 2150196
Author(s):  
Aly R. Seadawy ◽  
Khalid K. Ali ◽  
Jian-Guo Liu
Keyword(s):  
Schrodinger Equation ◽  
Dynamical Equation ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Nonlinear Schrodinger Equation ◽  
Optical Soliton ◽  
Modified Kudryashov Method ◽  
Kudryashov Method ◽  
Spatio Temporal ◽  
Temporal Dispersal

In this paper, we examine the Fokas–Lenells equation (FLE) that depicts the promulgation of ultra-short pulsation in visual fibers while confirming the terms of the following asymptotic arrangement beyond those indispensable for the nonlinear Schrödinger equation. In addition the model includes both spatio–temporal dispersal and self-steepening terms. Then, we discuss deep visual solutions of the FLE via taking the modified Kudryashov method and the extended tanh expansion method.

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