scholarly journals Concentration phenomenon of the endemic equilibrium of a reaction-diffusion-advection SIS epidemic model with spontaneous infection

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Chengxia Lei ◽  
Xinhui Zhou
Keyword(s):  
Infectious Disease ◽  
Reaction Diffusion ◽  
Endemic Equilibrium ◽  
Heterogeneous Environment ◽  
Small Diffusion ◽  
Susceptible Population ◽  
Asymptotic Behaviors ◽  
Sis Epidemic Model ◽  
Sis Epidemic ◽  
Spontaneous Infection

<p style='text-indent:20px;'>In this paper, we investigate the effect of spontaneous infection and advection for a susceptible-infected-susceptible epidemic reaction-diffusion-advection model in a heterogeneous environment. The existence of the endemic equilibrium is proved, and the asymptotic behaviors of the endemic equilibrium in three cases (large advection; small diffusion of the susceptible population; small diffusion of the infected population) are established. Our results suggest that the advection can cause the concentration of the susceptible and infected populations at the downstream, and the spontaneous infection can enhance the persistence of infectious disease in the entire habitat.</p>

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

scholarly journals Dynamics and asymptotic profiles of endemic equilibrium for two frequency-dependent SIS epidemic models with cross-diffusion

2018 ◽  
Vol 31 (1) ◽  
pp. 26-56 ◽  
Author(s):  
HUICONG LI ◽  
RUI PENG ◽  
TIAN XIANG
Keyword(s):  
Infectious Disease ◽  
Total Population ◽  
Initial Boundary ◽  
Endemic Equilibrium ◽  
Diffusion Term ◽  
Frequency Dependent ◽  
Susceptible Population ◽  
Cross Diffusion ◽  
Special Cases ◽  
Globally Stable

This paper is concerned with two frequency-dependent susceptible–infected–susceptible epidemic reaction–diffusion models in heterogeneous environment, with a cross-diffusion term modelling the effect that susceptible individuals tend to move away from higher concentration of infected individuals. It is first shown that the corresponding Neumann initial-boundary value problem in an n-dimensional bounded smooth domain possesses a unique global classical solution which is uniformly in-time bounded regardless of the strength of the cross-diffusion and the spatial dimension n. It is further shown that, even in the presence of cross-diffusion, the models still admit threshold-type dynamics in terms of the basic reproduction number $\mathcal {R}_0$ – i.e. the unique disease-free equilibrium is globally stable if $\mathcal {R}_0\lt1$, while if $\mathcal {R}_0\gt1$, the disease is uniformly persistent and there is an endemic equilibrium (EE), which is globally stable in some special cases with weak chemotactic sensitivity. Our results on the asymptotic profiles of EE illustrate that restricting the motility of susceptible population may eliminate the infectious disease entirely for the first model with constant total population but fails for the second model with varying total population. In particular, this implies that such cross-diffusion does not contribute to the elimination of the infectious disease modelled by the second one.

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