Results 41 to 50 of about 70,485 (205)

Lyapunov functions for SIR and SIRS epidemic models

Applied Mathematics Letters, 2010
The authors consider the planar system \[ \begin{aligned} {dI\over dt} &= (q-\beta I-\beta R)I,\\ {dR\over dt} &= \gamma I-\omega R\end{aligned}\tag{\(*\)} \] related to epidemic models. Let \(Q_*= (I_*, R_*)\) be a positive equilibrium of \((*)\). It is shown that \[ U(I,R):= I- I_*\ln I+ a(R- R_*)^2 \] with \(a:= \beta/2\gamma> 0\) is a Lyapunov ...
O’Regan, Suzanne M., Kelly, Thomas C., Korobeinikov, Andrei, O’Callaghan, Michael J.A., Pokrovskii, Alexei V.   +4 more
openaire   +1 more source

Stability and Immune Control Strategy of SIＲ Scale-free Network Model

Journal of Harbin University of Science and Technology, 2018
In order to study the effect of the vaccine immunization and the individual immigration on the spread behaviors of the SIＲ epidemic，the SIＲ epidemic model for complex networks is constructed. The equilibrium stability of complex networks with homogeneous
WANG Jing-nan, LU Lan-fen, GAO Xu, XU Yun-zhong, DING Yue-hang   +4 more
doaj   +1 more source

Optimal vaccination in a stochastic epidemic model of two non-interacting populations [PDF]

, 2014
Developing robust, quantitative methods to optimize resource allocations in response to epidemics has the potential to save lives and minimize health care costs. In this paper, we develop and apply a computationally efficient algorithm that enables us to
Alderson, David L., Carlson, Jean M., Stromberg, Sean, Yuan, Edwin C.   +3 more
core   +4 more sources

Analysis of SIR Epidemic Models with Sociological Phenomenon

SPORA: A Journal of Biomathematics, 2022
We propose two SIR models which incorporate sociological behavior of groups of individuals. It is these differences in behaviors which impose different infection rates on the individual susceptible populations, rather than biological differences. We compute the basic reproduction number for each model, as well as analyze the sensitivity of $R_0$ to ...
Allen, Robert F, Heller, Katherine C, Pons, Matthew A   +2 more
openaire   +3 more sources

Effect of a Vaccination against the Dengue Fever Epidemic in an Age Structure Population: From the Perspective of the Local and Global Stability Analysis

Mathematics, 2022
The effect of vaccination on the dengue fever epidemic described by an age structured modified SIR (Susceptible-Infected-Retired) model is studied using standard stability analysis.
Anusit Chamnan, Puntani Pongsumpun, I-Ming Tang, Napasool Wongvanich   +3 more
doaj   +1 more source

FastSIR Algorithm: A Fast Algorithm for simulation of epidemic spread in large networks by using SIR compartment model

, 2012
The epidemic spreading on arbitrary complex networks is studied in SIR (Susceptible Infected Recovered) compartment model. We propose our implementation of a Naive SIR algorithm for epidemic simulation spreading on networks that uses data structures ...
Albert, Albert, Alen Lančić, Barabasi, Broder, Broeck, Callaway, Colizza, Colizza, Cormen, Csardi, Dorogovtsev, Dorogovtsev, Eubank, Grassberger, Hethcote, Hrvoje Štefančić, Kenah, Kermack, Lancic, Liljeros, Meyers, Mile Šikić, Mollison, Newman, Newman, Nino Antulov-Fantulin, Pastor-Satorras, Satsuma, Saumell-Mendiola, Shaw, Tizzoni, Vespignani, Vitter, Wang, Watts   +35 more
core   +1 more source

Epidemic cycling in a multi-strain SIRS epidemic network model [PDF]

Theoretical Biology and Medical Modelling, 2016
One common observation in infectious diseases caused by multi-strain pathogens is that both the incidence of all infections and the relative fraction of infection with each strain oscillate with time (i.e., so-called Epidemic cycling). Many different mechanisms have been proposed for the pervasive nature of epidemic cycling. Nevertheless, the two facts
openaire   +2 more sources

Approximate and Parametric Solutions to SIR Epidemic Model

Axioms
This article provides a detailed exploration of the SIR epidemic model, starting with its meticulous formulation. The study employs a novel approach called the upper and lower bounds technique to approximate the solution to the SIR model, providing ...
Lazhar Bougoffa, Smail Bougouffa, Ammar Khanfer   +2 more
doaj   +1 more source

Network-based analysis of stochastic SIR epidemic models with random and proportionate mixing

, 2007
In this paper, we outline the theory of epidemic percolation networks and their use in the analysis of stochastic SIR epidemic models on undirected contact networks.
Kenah, Eben, Robins, James M.
core   +6 more sources

The deterministic Kermack-McKendrick model bounds the general stochastic epidemic [PDF]

, 2016
We prove that, for Poisson transmission and recovery processes, the classic Susceptible $\to$ Infected $\to$ Recovered (SIR) epidemic model of Kermack and McKendrick provides, for any given time $t>0$, a strict lower bound on the expected number of ...
Ball, Frank G., Sharkey, Kieran J., Wilkinson, Robert R.   +2 more
core   +3 more sources