STABILITY ANALYSIS AND APPROXIMATE SOLUTION OF SIR EPIDEMIC MODEL WITH CROWLEY-MARTIN TYPE FUNCTIONAL RESPONSE AND HOLLING TYPE-Ⅱ TREATMENT RATE BY USING HOMOTOPY ANALYSIS METHOD

DOI10.11948/20190239zbMath1455.34039OpenAlexW3086012612MaRDI QIDQ4964209

Mohammad Ghoreishi, Jian Zu, Parvaiz Ahmad Naik

Publication date: 25 February 2021

Published in: Journal of Applied Analysis & Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.11948/20190239

zbMATH Keywords

stability analysishomotopy analysis methodSIR epidemic modelauxiliary parameter \(\hbar\)Crowley-Martin-type incidence rateHolling type-II treatment ratereproduction number \(\mathfrak{R}_0\)

Mathematics Subject Classification ID

Epidemiology (92D30) Bifurcation theory for ordinary differential equations (34C23) Stability of solutions to ordinary differential equations (34D20) Qualitative investigation and simulation of ordinary differential equation models (34C60) Global stability of solutions to ordinary differential equations (34D23)

Related Items

Chaotic dynamics of a fractional order HIV-1 model involving AIDS-related cancer cells ⋮ Complex dynamics of a discrete-time Bazykin-Berezovskaya prey-predator model with a strong Allee effect ⋮ Modeling and numerical investigation of fractional‐order bovine babesiosis disease ⋮ European option pricing models described by fractional operators with classical and generalized<scp>Mittag‐Leffler</scp>kernels ⋮ Dynamical analysis of a discrete-time SIR epidemic model ⋮ Global dynamics and bifurcation analysis of a fractional‐order SEIR epidemic model with saturation incidence rate ⋮ Complex dynamics of a discrete‐time seasonally forced SIR epidemic model ⋮ Bifurcations of a discrete-time SIR epidemic model with logistic growth of the susceptible individuals ⋮ Complex dynamics of a discrete-time SIR model with nonlinear incidence and recovery rates ⋮ Global behavior of a multi-group SEIR epidemic model with age structure and spatial diffusion ⋮ Stability analysis of a fractional-order cancer model with chaotic dynamics ⋮ Global dynamics of a fractional-order SIR epidemic model with memory ⋮ Almost periodic solutions for a SVIR epidemic model with relapse ⋮ Threshold dynamics and optimal control on an age-structured SIRS epidemic model with vaccination ⋮ Theoretical analysis of a measles model with nonlinear incidence functions ⋮ Analytical solution of the SIR-model for the temporal evolution of epidemics: part B. Semi-time case

Cites Work

• Unnamed Item
• Unnamed Item
• Activation of effector immune cells promotes tumor stochastic extinction: a homotopy analysis approach
• Persistence and global stability of Bazykin predator-prey model with Beddington-DeAngelis response function
• Application of the homotopy analysis method for solving a model for HIV infection of CD4\(^{+}\) T-cells
• Dynamics of an SIR epidemic model with limited medical resources revisited
• The comparison between homotopy analysis method and optimal homotopy asymptotic method for nonlinear age-structured population models
• Analysis of a stage-structured predator-prey model with Crowley-Martin function
• Solution of a strongly coupled reaction-diffusion system by the homotopy analysis method
• Optimal homotopy analysis of a chaotic HIV-1 model incorporating AIDS-related cancer cells
• Global results for an SIRS model with vaccination and isolation
• Some epidemiological models with nonlinear incidence
• A fractional-order differential equation model of HIV infection of \(CD4^{+}\) T-cells
• Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models
• Nonlinear systems. Analysis, stability, and control
• Bifurcations in an epidemic model with constant removal rate of the infectives
• A delay-differential equation model of HIV infection of \(\text{CD}4^+\) T-cells
• Semianalytical solutions by homotopy analysis method for EIAV infection with stability analysis
• Dynamical models of tuberculosis and their applications
• A disease transmission model in a nonconstant population
• Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
• Solving a modified nonlinear epidemiological model of computer viruses by homotopy analysis method
• Modeling the role of acquired immune response and antiretroviral therapy in the dynamics of HIV infection
• On the convergence of the homotopy analysis method for inner-resonance of tangent nonlinear cushioning packaging system with critical components
• Estimating the approximate analytical solution of HIV viral dynamic model by using homotopy analysis method
• Transmission dynamics of an influenza model with vaccination and antiviral treatment
• Mathematical analysis of the global dynamics of a model for HIV infection of CD4\(^{+}\) T cells
• Backward bifurcation of an epidemic model with treatment
• Periodicity in an epidemic model with a generalized non-linear incidence
• Comparison between the homotopy analysis method and homotopy perturbation method
• Global Analysis in a Predator-Prey System with Nonmonotonic Functional Response
• The Mathematics of Infectious Diseases
• Global Stability of Infectious Disease Models Using Lyapunov Functions
• MODELING AND ANALYSIS OF AN SEIR MODEL WITH DIFFERENT TYPES OF NONLINEAR TREATMENT RATES
• Bifurcations of an epidemic model with non-linear incidence and infection-dependent removal rate
• An analytic solution of projectile motion with the quadratic resistance law using the homotopy analysis method
• Permanence and stability of a stage-structured predator-prey model

This page was built for publication: STABILITY ANALYSIS AND APPROXIMATE SOLUTION OF SIR EPIDEMIC MODEL WITH CROWLEY-MARTIN TYPE FUNCTIONAL RESPONSE AND HOLLING TYPE-Ⅱ TREATMENT RATE BY USING HOMOTOPY ANALYSIS METHOD