Global Dynamics of a Periodic SEIRS Model with General Incidence Rate

Ávila-Vales, Eric; Rivero-Esquivel, Erika; García-Almeida, Gerardo E.

doi:10.1155/2017/5796958

Cited by 9 publications

(6 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Similar works and results can be found in [6,18,27,3]. Nonlinear incidences of the form uϕ (v) were investigated in [7,4,25,16,5] among numerous other studies. However, these studies only considered the simple diffusion-free case, which disregards the distribution of individuals within their respective spatial domain.…”

Section: Introductionsupporting

confidence: 61%

Global and local asymptotic stability of an epidemic reaction-diffusion model with a nonlinear incidence

Djebara¹,

Douaifia²,

Abdelmalek³

et al. 2020

Preprint

View full text Add to dashboard Cite

The aim of this paper is to study the dynamics of a reaction-diffusion SIS (susceptible-infectious-susceptible) epidemic model with a nonlinear incidence rate describing the transmission of a communicable disease between individuals. We prove that the proposed model has two steady states under one condition. By analyzing the eigenvalues and using the Routh-Hurwitz criterion and an appropriately constructed Lyapunov functional, we establish the local and global asymptotic stability of the non negative constant steady states subject to the basic reproduction number being greater than unity and of the disease-free equilibrium subject to the basic reproduction number being smaller than or equal to unity in ODE case. By applying an appropriately constructed Lyapunov functional, we identify the condition of the global stability in the PDE case. Finally, we present some numerical examples illustrating and confirming the analytical results obtained throughout the paper.

show abstract

Section: Introductionsupporting

confidence: 61%

Global and local asymptotic stability of an epidemic reaction-diffusion model with a nonlinear incidence

Djebara¹,

Douaifia²,

Abdelmalek³

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…There are several works where the study of positive periodic solutions is developed, for instance in [13,[19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. In particular, recently in [13] was proved the existence of at one positive periodic solution of the following system modeling the dynamics of a computer virus…”

Section: Related Workmentioning

confidence: 99%

“…Proof. In order to prove the Lemma we apply the Definition 1 or more precisely we prove that L satisfy Equation (20).…”

Section: Is a Fredholm Operator Of Index Zeromentioning

confidence: 99%

Analysis of a SEIR-KS Mathematical Model For Computer Virus Propagation in a Periodic Environment

et al. 2020

View full text Add to dashboard Cite

In this work we develop a study of positive periodic solutions for a mathematical model of the dynamics of computer virus propagation. We propose a generalized compartment model of SEIR-KS type, since we consider that the population is partitioned in five classes: susceptible (S); exposed (E); infected (I); recovered (R); and kill signals (K), and assume that the rates of virus propagation are time dependent functions. Then, we introduce a sufficient condition for the existence of positive periodic solutions of the generalized SEIR-KS model. The proof of the main results are based on a priori estimates of the SEIR-KS system solutions and the application of coincidence degree theory. Moreover, we present an example of a generalized system satisfying the sufficient condition.

show abstract

“…Other interesting works related to periodic solutions include seasonally forced SIR and SEIRS models with impact of media coverage are presented in Zu and Wang ( 2015 ), Ávila-Vales et al. ( 2017 ).…”

Section: Introductionmentioning

confidence: 99%

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

2021

View full text Add to dashboard Cite

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.

show abstract

Global Dynamics of a Periodic SEIRS Model with General Incidence Rate

Cited by 9 publications

References 25 publications

Global and local asymptotic stability of an epidemic reaction-diffusion model with a nonlinear incidence

Global and local asymptotic stability of an epidemic reaction-diffusion model with a nonlinear incidence

Analysis of a SEIR-KS Mathematical Model For Computer Virus Propagation in a Periodic Environment

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

Contact Info

Product

Resources

About