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Related papers: Backward bifurcation in SIRS malaria model

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SIRS models capture transmission dynamics of infectious diseases for which immunity is not lifelong. Extending these models by a W compartment for individuals with waning immunity, the boosting of the immune system upon repeated exposure…

Populations and Evolution · Quantitative Biology 2022-01-19 Richmond Opoku-Sarkodie , Ferenc A. Bartha , Mónika Polner , Gergely Röst

We investigate the bifurcation structure of equilibria in a class of non-autonomous ordinary differential equations governed by a season length parameter, $\tau$, which determines the alternation between growth and decline dynamics. This…

Dynamical Systems · Mathematics 2025-07-09 Gonzalo Galiano , Julián Velasco

The SIRS model with constant vaccination and immunity waning rates is well known to show a transition from a disease-free to an endemic equilibrium as the basic reproduction number $r_0$ is raised above threshold. It is shown that this…

Populations and Evolution · Quantitative Biology 2024-10-28 Florian Nill

There are few adapted SIR models in the literature that combine vaccination and logistic growth. In this article, we study bifurcations of a SIR model where the class of Susceptible individuals grows logistically and has been subject to…

Dynamical Systems · Mathematics 2023-04-26 João P. S. Maurício de Carvalho , Alexandre A. Rodrigues

In this paper, we investigate an SVIRS epidemic model that incorporates both temporary immunity and an age-structured recovery process. By reformulating the system as a non-densely defined abstract Cauchy problem, we establish the existence…

Dynamical Systems · Mathematics 2025-12-03 Songbo Hou , Xinxin Tian

This paper demonstrates input-to-state stability (ISS) of the SIR model of infectious diseases with respect to the disease-free equilibrium and the endemic equilibrium. Lyapunov functions are constructed to verify that both equilibria are…

Optimization and Control · Mathematics 2020-06-09 Hiroshi Ito

We study the global dynamics of a reaction-diffusion SEIR infection model with distributed delay and nonlinear incidence rate. The well-posedness of the proposed model is proved. By means of Lyapunov functionals, we show that the disease…

Populations and Evolution · Quantitative Biology 2022-04-21 Abdesslem Lamrani Alaoui , Moulay Rchid Sidi Ammi , Mouhcine Tilioua , Delfim F. M. Torres

This research paper introduces an SQIR-V epidemic model to investigate the transmission of infectious diseases. Particular attention is paid to the roles of vaccination and quarantine (incorporating physical distancing interventions) in…

Dynamical Systems · Mathematics 2026-03-26 Mehdi Bouziane , Silia Bercisse , Abdennasser Chekroun , Simon Girel

A comparative stochastic and deterministic study of a family of SEIRS epidemic dynamic models for malaria is presented. The family type is determined by the qualitative behavior of the nonlinear incidence rates of the disease. Furthermore,…

Populations and Evolution · Quantitative Biology 2018-09-12 Divine Wanduku

Diffusion models have emerged as powerful tools for solving inverse problems, yet prior work has primarily focused on observations with Gaussian measurement noise, restricting their use in real-world scenarios. This limitation persists due…

Machine Learning · Statistics 2025-02-11 Alessandro Micheli , Mélodie Monod , Samir Bhatt

In this paper we describe the dynamics of a vector-borne relapsing disease, such as tick-borne relapsing fever, using the methods of compartmental models. After some motivation, model description, and a brief overview of the theory of…

Dynamical Systems · Mathematics 2016-08-24 Cody Palmer , Erin Landguth , Emily Stone , Tammi Johnson

This study examines the behavior of solutions in a multi-patch epidemic model that includes a saturation incidence mechanism. When the fatality rate due to the disease is not null, our findings show that the solutions of the model tend to…

Populations and Evolution · Quantitative Biology 2024-09-19 Yawo Ezunkpe , Cynthia T. Nnolum , Rachidi B. Salako , Shuwen Xue

In this paper, we develop a dynamic model of HIV infection that incorporates latent hosts, cytotoxic T lymphocyte (CTL) immunity, saturated incidence rates, and two transmission mechanisms: virus-to-cell and cell-to-cell transmission. The…

Dynamical Systems · Mathematics 2025-11-25 Songbo Hou , Xinxin Tian

The main purpose of this paper is to study the local dynamics and bifurcations of a discrete-time SIR epidemiological model. The existence and stability of disease-free and endemic fixed points are investigated along with a fairly complete…

Dynamical Systems · Mathematics 2021-08-05 Johan Hallberg Szabadváry , Yishao Zhou

This paper deals with a new epidemiological model of SIRS with stochastic perturbations. The primary objective is to establish the existence of a unique non-negative nonlocal solution. Using the basic reproduction number $\mathscr{R}_0$…

Dynamical Systems · Mathematics 2025-03-10 Achraf Zinihi , Moulay Rchid Sidi Ammi , Matthias Ehrhardt

One of the main causes of death around the globe is malaria. Researchers have sought to develop predictive models for malaria outbreaks based on meteorological data, climate data and the breeding cycle of Plasmodium, the causative agent of…

Other Quantitative Biology · Quantitative Biology 2026-05-20 Mary Opokua Ansong , Asare Yaw Obeng , Samuel King Opoku

TThis paper presents the dynamics of mosquitoes and humans, with general nonlinear incidence rate and multiple distributed delays for the disease. The model is a SEIRS system of delay differential equations. The normalized dimensionless…

Dynamical Systems · Mathematics 2020-05-05 Divine Wanduku

Malaria constitutes an important cause of human mortality. After 2009 Greece experienced a resurgence of malaria. Here, we develop a modelbased framework that integrates entomological, geographical, social and environmental evidence in…

This paper studies the dynamics of a network-based SIRS epidemic model with vaccination and a nonmonotone incidence rate. This type of nonlinear incidence can be used to describe the psychological or inhibitory effect from the behavioral…

Populations and Evolution · Quantitative Biology 2018-11-14 Lijun Liu , Xiaodan Wei , Naimin Zhang

The existence of a die-out threshold (different from the classic disease-invasion one) defining a region of slow extinction of an epidemic has been proved elsewhere for susceptible-aware-infectious-susceptible models without awareness…

Quantitative Methods · Quantitative Biology 2016-10-19 David Juher , Istvan Z. Kiss , Joan Saldana