The spreading speed of an SIR epidemic model with nonlocal dispersal

2020 ◽  
Vol 120 (1-2) ◽  
pp. 163-174 ◽  
Author(s):  
Jong-Shenq Guo ◽  
Amy Ai Ling Poh ◽  
Masahiko Shimojo
Keyword(s):  
Comparison Principle ◽  
Epidemic Model ◽  
Sir Model ◽  
Spreading Speed ◽  
Sir Epidemic Model ◽  
Nonlocal Dispersal ◽  
Sir Epidemic ◽  
Scalar Equations ◽  
Asymptotic Spreading

In this paper, we study an SIR epidemic model with nonlocal dispersal. We study the case with vital dynamics so that a renewal of the susceptible individuals is taken into account. We characterize the asymptotic spreading speed to estimate how fast the disease under consideration spreads. Due to the lack of comparison principle for the SIR model, our proof is based on a delicate analysis of related problems with nonlocal scalar equations.

scholarly journals Fractional-Order SIR Epidemic Model for Transmission Prediction of COVID-19 Disease

2020 ◽  
Vol 10 (23) ◽  
pp. 8316
Author(s):  
Kamil Kozioł ◽  
Rafał Stanisławski ◽  
Grzegorz Bialic
Keyword(s):  
Fractional Order ◽  
Epidemic Model ◽  
Dynamic Properties ◽  
Sir Model ◽  
Domain Model ◽  
Sir Epidemic Model ◽  
Step Method ◽  
Order Difference ◽  
Sir Epidemic ◽  
The Time Domain

In this paper, the fractional-order generalization of the susceptible-infected-recovered (SIR) epidemic model for predicting the spread of the COVID-19 disease is presented. The time-domain model implementation is based on the fixed-step method using the nabla fractional-order difference defined by Grünwald-Letnikov formula. We study the influence of fractional order values on the dynamic properties of the proposed fractional-order SIR model. In modeling the COVID-19 transmission, the model’s parameters are estimated while using the genetic algorithm. The model prediction results for the spread of COVID-19 in Italy and Spain confirm the usefulness of the introduced methodology.

scholarly journals Traveling Waves in a Nonlocal Dispersal SIR Model with Standard Incidence Rate and Nonlocal Delayed Transmission

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 641 ◽  
Author(s):  
Kuilin Wu ◽  
Kai Zhou
Keyword(s):  
Incidence Rate ◽  
Traveling Wave ◽  
Epidemic Model ◽  
Reaction System ◽  
Traveling Wave Solutions ◽  
Sir Epidemic Model ◽  
Nonlocal Dispersal ◽  
Sir Epidemic ◽  
Wave Solutions ◽  
Minimal Wave Speed

In this paper, we study the traveling wave solutions for a nonlocal dispersal SIR epidemic model with standard incidence rate and nonlocal delayed transmission. The existence and nonexistence of traveling wave solutions are determined by the basic reproduction number of the corresponding reaction system and the minimal wave speed. To prove these results, we apply the Schauder’s fixed point theorem and two-sided Laplace transform. The main difficulties are that the complexity of the incidence rate in the epidemic model and the lack of regularity for nonlocal dispersal operator.

DYNAMIC ANALYSIS OF AN SIR MODEL WITH STOCHASTIC PERTURBATIONS

2013 ◽  
Vol 06 (06) ◽  
pp. 1350041
Author(s):  
ZHENJIE LIU ◽  
JINLIANG WANG ◽  
YALAN XU ◽  
GUOQIANG LI
Keyword(s):  
Epidemic Model ◽  
Lyapunov Functions ◽  
Sir Model ◽  
Sir Epidemic Model ◽  
Stochastic Perturbations ◽  
Sir Epidemic ◽  
Stochastic Epidemic ◽  
Differential Infectivity ◽  
Global Positive Solution ◽  
Stochastic Epidemic Model

In this paper, we present a differential infectivity SIR epidemic model with modified saturation incidences and stochastic perturbations. We show that the stochastic epidemic model has a unique global positive solution, and we utilize stochastic Lyapunov functions to show the asymptotic behavior of the solution.

scholarly journals Traveling waves for a nonlocal dispersal SIR epidemic model with the mass action infection mechanism

2021 ◽  
Author(s):  
Xin Wu ◽  
Zhaohai Ma
Keyword(s):  
Equilibrium State ◽  
Traveling Waves ◽  
Epidemic Model ◽  
Mass Action ◽  
Sir Epidemic Model ◽  
Nonlocal Dispersal ◽  
New Model ◽  
Infection Mechanism ◽  
Sir Epidemic ◽  
Lasalle Theorem

This paper is concerned with a nonlocal dispersal susceptible–infected–recovered (SIR) epidemic model adopted with the mass action infection mechanism. We mainly study the existence and non-existence of traveling waves connecting the infection-free equilibrium state and the endemic equilibrium state. The main difficulties lie in the fact that the semiflow generated here does not admit the order-preserving property. Meanwhile, this new model brings some new challenges due to the unboundedness of the nonlinear term. We overcome these difficulties to obtain the boundedness of traveling waves with the speed $c>c_{\min}$ by some analysis techniques firstly and then prove the existence of traveling waves by employing Lyapunov–LaSalle theorem and Lebesgue dominated convergence theorem. By utilizing a approximating method, we study the existence of traveling waves with the critical wave speed $c_{\min}$. Our results on this new model may provide some implications on disease modelling and controls.

A MATHEMATICAL DESCRIPTION OF THE CRITICAL POINT IN PHASE TRANSITIONS

2013 ◽  
Vol 24 (10) ◽  
pp. 1350065 ◽  
Author(s):  
AYSE HUMEYRA BILGE ◽  
ONDER PEKCAN
Keyword(s):  
Phase Transition ◽  
Critical Point ◽  
Growth Curve ◽  
Epidemic Model ◽  
Sir Model ◽  
Transition Curve ◽  
Logistic Growth ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Sigmoidal Curve

Let y(x) be a smooth sigmoidal curve, y(n) be its nth derivative and {xm,i} and {xa,i}, i = 1,2,…, be the set of points where respectively the derivatives of odd and even order reach their extreme values. We argue that if the sigmoidal curve y(x) represents a phase transition, then the sequences {xm,i} and {xa,i} are both convergent and they have a common limit xc that we characterize as the critical point of the phase transition. In this study, we examine the logistic growth curve and the Susceptible-Infected-Removed (SIR) epidemic model as typical examples of symmetrical and asymmetrical transition curves. Numerical computations indicate that the critical point of the logistic growth curve that is symmetrical about the point (x0, y0) is always the point (x0, y0) but the critical point of the asymmetrical SIR model depends on the system parameters. We use the description of the sol–gel phase transition of polyacrylamide-sodium alginate (SA) composite (with low SA concentrations) in terms of the SIR epidemic model, to compare the location of the critical point as described above with the "gel point" determined by independent experiments. We show that the critical point tc is located in between the zero of the third derivative ta and the inflection point tm of the transition curve and as the strength of activation (measured by the parameter k/η of the SIR model) increases, the phase transition occurs earlier in time and the critical point, tc, moves toward ta.

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