scholarly journals An infection age-space structured SIR epidemic model with Neumann boundary condition

2018 ◽  
Vol 99 (11) ◽  
pp. 1972-1985 ◽  
Author(s):  
Abdennasser Chekroun ◽  
Toshikazu Kuniya
Keyword(s):  
Boundary Condition ◽  
Epidemic Model ◽  
Neumann Boundary Condition ◽  
Neumann Boundary ◽  
Sir Epidemic Model ◽  
Infection Age ◽  
Sir Epidemic

An infection age-space-structured SIR epidemic model with Dirichlet boundary condition

2019 ◽  
Vol 14 (5) ◽  
pp. 505 ◽  
Author(s):  
Abdennasser Chekroun ◽  
Toshikazu Kuniya
Keyword(s):  
Boundary Condition ◽  
Steady State ◽  
Dirichlet Boundary Condition ◽  
Epidemic Model ◽  
Dirichlet Boundary ◽  
Upper And Lower Solutions ◽  
Sir Epidemic Model ◽  
Infection Age ◽  
Sir Epidemic ◽  
Disease Free

In this paper, we are concerned with the global asymptotic behavior of an SIR epidemic model with infection age-space structure. Under the homogeneous Dirichlet boundary condition, we first reformulate the model into the coupled reaction-diffusion and difference system by using the method of characteristics. We then obtain the spatially heterogeneous disease-free steady state and define the basic reproduction number ℛ0 by the spectral radius of the next generation operator. We then show the existence and uniqueness of the global classical solution by constructing suitable upper and lower solutions. As a threshold result, we establish that the disease-free steady state is globally attractive if ℛ0 < 1, whereas the system is uniformly weakly persistent in norm if ℛ0 > 1. Finally, numerical simulations are exhibited to illustrate our theoretical results together with how to compute ℛ0.

Analisis Titik Kesetimbangan Dan Kestabilan Penyebaran Penyakit Malaria di Distrik Manokwari Barat Berdasarkan Model Epidemik SIR

2012 ◽  
Vol 8 (2) ◽  
Author(s):  
Fandy Fandy ◽  
Andi Fajeriani Wyrasti ◽  
Tri Widjajanti
Keyword(s):  
Epidemic Model ◽  
Sir Epidemic Model ◽  
Endemic Diseases ◽  
Sir Epidemic

<em>Stability and equilibrium of malaria&rsquo;s epidemics in Manokwari Barat district based on SIR epidemic model will be discussed in this paper. The SIR epidemic model can be applied to make a model of endemic diseases like malaria. Based on this research, there are 2 types of the equilibrium of malaria&rsquo;s epidemics in Manokwari Barat District, endemic and non endemic point.</em>

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