Global stability analysis of an SVEIR epidemic model with general incidence rate

In this article, we study the dynamics of a new proposed age-structured population mathematical model driven by a seasonal forcing function that takes into account the variability of the climate. We introduce a generalized force of infection function to study different potential disease outcomes. Using nonlinear analysis tools and differential inequalities theorems, we obtain sufficient conditions that guarantee the existence of a positive periodic solution. Moreover, we provide sufficient conditions that assure the global attractivity of the positive periodic solution. Numerical results corroborate the theoretical results in the sense that the solutions are positive and the periodic solution is a global attractor. This type of models are important, since they take into account the variability of the weather and the impact on some epidemics such as the current COVID-19 pandemic.

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“…Similar interesting models with some variants are also presented in Derrick and Van den Driessche ( 1993 ), Gao et al. ( 2018 ).…”

Section: Introductionsupporting

confidence: 70%

Nonlinear dynamics of a new seasonal epidemiological model with age-structure and nonlinear incidence rate

2021

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“…dan beberapa penelitian tentang model SVEIR, salah satunya Saputri (2014) menganalisis kestabilan model SVEIR pada penyakit difteri. Kemudian (Gao et al, 2018) menganalisis stabilitas global dari model epidemi SVEIR dengan tingkat kejadian umum Selain itu juga, (Nabti & Ghanbari, 2021) (3)…”

Section: Pendahuluanunclassified

Pemodelan Matematika Penyebaran Covid-19 Dengan Model Sveir

Septiansyah

Karim

Yulida

2022

JMMTE

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Coronavirus disease 2019 or also known as Covid-19 is a disease caused by a type of coronavirus called Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) or better known as the corona virus. Covid-19 become a pandemic since 2020 and has been widely studied, one of which is in mathematical modeling. In this study, the spread of Covid-19 is modeled using the SVEIR (Susceptible, Vaccination, Exposed, Infected, and Recovered) model. The purpose of this study explains the formation of the Covid-19 SVEIR model, determines the equilibrium point, determines the basic reproduction number, and analyzes the stability of the Covid-19 SVEIR model. The purpose of this study explains the formation of the Covid-19 SVEIR model, determines the equilibrium point, the basic reproduction number, and analyzes the stability of the Covid-19 SVEIR model. The result of this study is to explain the formation of the Covid-19 SVEIR model and obtained two equilibrium points, the disease-free equilibrium point and the endemic equilibrium point. Furthermore, the basic reproduction number is obtained through the Next Generation Matrix method. The results of the stability analysis at the disease-free equilibrium point were locally asymptotically stable with conditions while at the endemic equilibrium point local asymptotically stable with conditions . The natural death rate is greater than the effective contact rate. A numerical simulation is presented to show a comparison spread of Covid-19 by providing different levels of vaccine effectiveness using the Runge-Kutta Order method.

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“…Anderson and May [2] were the pioneers for investigating the invasion, persistence, and spread of infectious diseases by formulating an eco-epidemiological prey-predator model. At recent times, many researchers have proposed and studied epidemic and eco-epidemiological models [3] , [4] , [5] , [6] , [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] , [15] . For example, Shaikh et al [6] have investigated the dynamics of an eco-epidemiological system with disease in competitive prey species.…”

Section: Introductionmentioning

confidence: 99%

Stability and bifurcation analysis of a diffusive modified Leslie-Gower prey-predator model with prey infection and Beddington DeAngelis functional response

Melese

Feyissa

2021

Heliyon

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In this paper, we present and analyze a spatio-temporal eco-epidemiological model of a prey predator system where prey population is infected with a disease. The prey population is divided into two categories, susceptible and infected. The susceptible prey is assumed to grow logistically in the absence of disease and predation. The predator population follows the modified Leslie-Gower dynamics and predates both the susceptible and infected prey population with Beddington-DeAngelis and Holling type II functional responses, respectively. The boundedness of solutions, existence and stability conditions of the biologically feasible equilibrium points of the system both in the absence and presence of diffusion are discussed. It is found that the disease can be eradicated if the rate of transmission of the disease is less than the death rate of the infected prey. The system undergoes a transcritical and pitchfork bifurcation at the Disease Free Equilibrium Point when the prey infection rate crosses a certain threshold value. Hopf bifurcation analysis is also carried out in the absence of diffusion, which shows the existence of periodic solution of the system around the Disease Free Equilibrium Point and the Endemic Equilibrium Point when the ratio of the rate of intrinsic growth rate of predator to prey crosses a certain threshold value. The system remains locally asymptotically stable in the presence of diffusion around the disease free equilibrium point once it is locally asymptotically stable in the absence of diffusion. The Analytical results show that the effect of diffusion can be managed by appropriately choosing conditions on the parameters of the local interaction of the system. Numerical simulations are carried out to validate our analytical findings.

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Global stability analysis of an SVEIR epidemic model with general incidence rate

Cited by 15 publications

References 44 publications

Nonlinear dynamics of a new seasonal epidemiological model with age-structure and nonlinear incidence rate

Nonlinear dynamics of a new seasonal epidemiological model with age-structure and nonlinear incidence rate

Pemodelan Matematika Penyebaran Covid-19 Dengan Model Sveir

Stability and bifurcation analysis of a diffusive modified Leslie-Gower prey-predator model with prey infection and Beddington DeAngelis functional response

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