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Related papers: Oscillation in the SIRS model

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We study two simple mathematical models of the epidemic. At first, we study the repetitive infection spreading in a simplified SIRS model including the effect of the decay of the acquired immune. The model is an intermediate model of the…

Populations and Evolution · Quantitative Biology 2024-03-13 Hidetsugu Sakaguchi , Keito Yamasaki

Time varying susceptibility of host at individual level due to waning and boosting immunity is known to induce rich long-term behavior of disease transmission dynamics. Meanwhile, the impact of the time varying heterogeneity of host…

Populations and Evolution · Quantitative Biology 2018-08-28 Yukihiko Nakata , Ryosuke Omori

Undulation of infection levels, usually called waves, are not well understood. In this paper we propose a mathematical model that exhibits undulation and decay towards a stable state. The model is a re-interpretation of the original…

Populations and Evolution · Quantitative Biology 2022-06-08 Niko Sauer

The stochastic SIRS model is a continuous-time Markov chain modelling the spread of infectious diseases with temporary immunity, in a homogeneously-mixing population of fixed size $N$. We study the scaling behaviour of the extinction time…

Probability · Mathematics 2021-01-14 Jingran Zhai

We propose two stochastic models for the Coronavirus pandemic. The statistical properties of the models, in particular the correlation functions and the probability density function, have duly been computed. Our models, which generalises a…

Medical Physics · Physics 2020-12-04 Giorgio Sonnino , Fernando Mora , Pasquale Nardone

We study the SIRS (Susceptible-Infected-Recovered-Susceptible) spreading processes over complex networks, by considering its exact $3^n$-state Markov chain model. The Markov chain model exhibits an interesting connection with its $2n$-state…

Social and Information Networks · Computer Science 2016-03-17 Navid Azizan Ruhi , Babak Hassibi

In light of the continuing emergence of new SARS-CoV-2 variants and vaccines, we create a simulation framework for exploring possible infection trajectories under various scenarios. The situations of primary interest involve the interaction…

Populations and Evolution · Quantitative Biology 2022-01-10 Kory D. Johnson , Annemarie Grass , Daniel Toneian , Mathias Beiglböck , Jitka Polechová

An adaptive network model using SIS epidemic propagation with link-type dependent link activation and deletion is considered. Bifurcation analysis of the pairwise ODE approximation and the network-based stochastic simulation is carried out,…

Probability · Mathematics 2014-10-21 András Szabó-Solticzky , Luc Berthouze , Istvan Z. Kiss , Péter L. Simon

Many infectious diseases are comprised of multiple strains with examples including Influenza, tuberculosis, and Dengue virus. The time evolution of such systems is linked to a complex landscape shaped by interactions between competing…

Populations and Evolution · Quantitative Biology 2023-11-21 Nir Gavish , Musa Rabiu

We analyse an extended SIRS epidemic model in which immunity at the individual level wanes gradually at exponential rate, but where the waning rate may differ between individuals, for instance as an effect of differences in immune systems.…

Populations and Evolution · Quantitative Biology 2023-11-02 Mohamed El Khalifi , Tom Britton

The aim of this study is to propose a modified Susceptible-Exposed-Infectious-Removed (SEIR) model that describes the behaviour of symptomatic, asymptomatic and hospitalized patients of COVID-19 epidemic, including the effect of demographic…

Mathematical models of infectious diseases exhibit robust dynamics such as stable endemic or a disease-free equilibrium, or convergence of the solutions to periodic epidemic waves. The present work shows that the accuracy of such dynamics…

Applications · Statistics 2022-05-04 Hadeel AlQadi , Majid Bani-Yaghoub

We study the classic Susceptible-Infected-Recovered (SIR) model for the spread of an infectious disease. In this stochastic process, there are two competing mechanism: infection and recovery. Susceptible individuals may contract the disease…

Populations and Evolution · Quantitative Biology 2012-05-08 E. Ben-Naim , P. L. Krapivsky

Growing literatures on epidemic and rumor dynamics show that infection and information coevolve. We present a unified framework for modeling the spread of infection and information: a general class of interaction-driven fluid-limit models…

Populations and Evolution · Quantitative Biology 2025-11-05 K. M. D. Chan , D. T. Crommelin , M. R. H. Mandjes

What is the long term dynamics of the Covid-19 pandemic? How will it end? Here we constructed an infectious disease model with testing and analyzed the existence and stability of its endemic states. For a large parameter set, including…

Populations and Evolution · Quantitative Biology 2023-11-16 Bo Deng , Chayu Yang

At the time of writing, the ongoing COVID-19 pandemic, caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), had already resulted in more than thirty-two million cases infected and more than one million deaths worldwide.…

Optimization and Control · Mathematics 2023-03-22 Chung-Han Hsieh

This paper is devoted to the study of a stochastic epidemiological model which is a variant of the SIR model to which we add an extra factor in the transition rate from susceptible to infected accounting for the inflow of infection due to…

Analysis of PDEs · Mathematics 2021-06-29 Gadi Fibich , Samuel Nordmann

The classic SIR model of epidemic dynamics is solved completely by quadratures, including a time integral transform expanded in a series of incomplete gamma functions. The model is also generalized to arbitrary time-dependent infection…

Populations and Evolution · Quantitative Biology 2020-10-07 E. Sadurní , G. Luna-Acosta

The susceptible-infectious-recovered (SIR) model describes the evolution of three species of individuals which are subject to an infection and recovery mechanism. A susceptible $S$ can become infectious with an infection rate $\beta$ by an…

Statistical Mechanics · Physics 2008-06-30 Gunter M. Schütz , Marian Brandau , Steffen Trimper

This technical report addresses a pressing issue in the trajectory of the coronavirus outbreak; namely, the rate at which effective immunity is lost following the first wave of the pandemic. This is a crucial epidemiological parameter that…