Pattern Dynamics of an SIS Epidemic Model with Nonlocal Delay

2019 ◽  
Vol 29 (02) ◽  
pp. 1950027 ◽  
Author(s):  
Zun-Guang Guo ◽  
Li-Peng Song ◽  
Gui-Quan Sun ◽  
Can Li ◽  
Zhen Jin
Keyword(s):  
Epidemic Model ◽  
Sufficient Conditions ◽  
Average Density ◽  
Reaction Diffusion Equation ◽  
Spatial Average ◽  
Stripe Pattern ◽  
Sis Epidemic Model ◽  
Nonlocal Delay ◽  
Pattern Dynamics ◽  
Sis Epidemic

In this paper, we study an SIS epidemic model with nonlocal delay based on reaction–diffusion equation. The spatiotemporal distribution of the model solution is studied in detail, and sufficient conditions for the occurrence of the Turing pattern were obtained using the analysis of Turing instability. It was found that the delay not only prohibited the spread of infectious disease, but also had great effects on the spatial steady-state patterns. More specifically, the spatial average density of the infected populations will decrease, as well the width of the stripe pattern will increase as delay increases. When the delay increases to a certain value, the stripe pattern changes to the mixed pattern. The results in this work provide new theoretical guidance for the prevention and treatment of infectious diseases.

scholarly journals Pattern Dynamics of Nonlocal Delay SI Epidemic Model with the Growth of the Susceptible following Logistic Mode

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Zun-Guang Guo ◽  
Jing Li ◽  
Can Li ◽  
Juan Liang ◽  
Yiwei Yan
Keyword(s):  
Time Delay ◽  
Epidemic Model ◽  
Turing Instability ◽  
Average Density ◽  
Linear Stability Theory ◽  
Susceptible Population ◽  
Nonlocal Delay ◽  
Pattern Dynamics ◽  
And Control ◽  
Theoretical Results

In this paper, we investigate pattern dynamics of a nonlocal delay SI epidemic model with the growth of susceptible population following logistic mode. Applying the linear stability theory, the condition that the model generates Turing instability at the endemic steady state is analyzed; then, the exact Turing domain is found in the parameter space. Additionally, numerical results show that the time delay has key effect on the spatial distribution of the infected, that is, time delay induces the system to generate stripe patterns with different spatial structures and affects the average density of the infected. The numerical simulation is consistent with the theoretical results, which provides a reference for disease prevention and control.

scholarly journals An SIS epidemic model with time delay and stochastic perturbation on heterogeneous networks

2021 ◽  
Vol 18 (5) ◽  
pp. 6790-6805
Author(s):  
Meici Sun ◽  
◽  
Qiming Liu
Keyword(s):  
Time Delay ◽  
Epidemic Model ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Sufficient Conditions ◽  
Stochastic Perturbation ◽  
Scale Free ◽  
Sis Epidemic Model ◽  
The Mean ◽  
Sis Epidemic

<abstract><p>An SIS epidemic model with time delay and stochastic perturbation on scale-free networks is established in this paper. And we derive sufficient conditions guaranteeing extinction and persistence of epidemics, respectively, which are related to the basic reproduction number $ R_0 $ of the corresponding deterministic model. When $ R_0 &lt; 1 $, almost surely exponential extinction and $ p $-th moment exponential extinction of epidemics are proved by Razumikhin-Mao Theorem. Whereas, when $ R_0 &gt; 1 $, the system is persistent in the mean under sufficiently weak noise intensities, which indicates that the disease will prevail. Finally, the main results are demonstrated by numerical simulations.</p></abstract>

Disease extinction and persistence in a discrete-time sis epidemic model with vaccination and varying population size

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4735-4747 ◽  
Author(s):  
Rahman Farnoosh ◽  
Mahmood Parsamanesh
Keyword(s):  
Population Size ◽  
Discrete Time ◽  
Epidemic Model ◽  
Jacobian Matrix ◽  
Sufficient Conditions ◽  
Period Doubling ◽  
System Of Difference Equations ◽  
Sis Epidemic Model ◽  
Necessary And Sufficient ◽  
Sis Epidemic

A discrete-time SIS epidemic model with vaccination is introduced and formulated by a system of difference equations. Some necessary and sufficient conditions for asymptotic stability of the equilibria are obtained. Furthermore, a sufficient condition is also presented. Next, bifurcations of the model including transcritical bifurcation, period-doubling bifurcation, and the Neimark-Sacker bifurcation are considered. In addition, these issues will be studied for the corresponding model with constant population size. Dynamics of the model are also studied and compared in detail with those found theoretically by using bifurcation diagrams, analysis of eigenvalues of the Jacobian matrix, Lyapunov exponents and solutions of the models in some examples.

scholarly journals Dynamics of a Nonautonomous Stochastic SIS Epidemic Model with Double Epidemic Hypothesis

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Haokun Qi ◽  
Lidan Liu ◽  
Xinzhu Meng
Keyword(s):  
Periodic Solution ◽  
Theoretical Analysis ◽  
Epidemic Model ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Nonlinear Incidence Rate ◽  
Sis Epidemic Model ◽  
Stochastic Sis Epidemic Model ◽  
Sis Epidemic

We investigate the dynamics of a nonautonomous stochastic SIS epidemic model with nonlinear incidence rate and double epidemic hypothesis. By constructing suitable stochastic Lyapunov functions and using Has’minskii theory, we prove that there exists at least one nontrivial positive periodic solution of the system. Moreover, the sufficient conditions for extinction of the disease are obtained by using the theory of nonautonomous stochastic differential equations. Finally, numerical simulations are utilized to illustrate our theoretical analysis.

scholarly journals Endemic Behaviour of SIS Epidemics with General Infectious Period Distributions

2014 ◽  
Vol 46 (01) ◽  
pp. 241-255 ◽  
Author(s):  
Peter Neal
Keyword(s):  
Epidemic Model ◽  
Branching Process ◽  
Endemic Equilibrium ◽  
Infectious Period ◽  
Sis Epidemic Model ◽  
Branching Process With Immigration ◽  
Sis Epidemic ◽  
Sis Epidemics ◽  
Surprising Observation

We study the endemic behaviour of a homogeneously mixing SIS epidemic in a population of size N with a general infectious period, Q, by introducing a novel subcritical branching process with immigration approximation. This provides a simple but useful approximation of the quasistationary distribution of the SIS epidemic for finite N and the asymptotic Gaussian limit for the endemic equilibrium as N → ∞. A surprising observation is that the quasistationary distribution of the SIS epidemic model depends on Q only through

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