scholarly journals Global dynamics of an epidemiological model with age-of-infection dependent treatment rate

2018 ◽  
Vol 67 (1) ◽  
pp. 125-140
Author(s):  
Gergely Röst ◽  
Toshikazu Kuniya ◽  
Seyed M. Moghadas ◽  
Jianhong Wu
Keyword(s):  
Epidemiological Model ◽  
Global Dynamics ◽  
Treatment Rate ◽  
Age Of Infection

scholarly journals Global Dynamics and Applications of an Epidemiological Model for Hepatitis C Virus Transmission in China

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Mingwang Shen ◽  
Yanni Xiao ◽  
Weike Zhou ◽  
Zhen Li
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Antiviral Treatment ◽  
Virus Transmission ◽  
Hcv Infection ◽  
Epidemiological Model ◽  
Global Dynamics ◽  
Treatment Rate ◽  
Chronic Stage ◽  
The Basic Reproduction Number

An epidemiological model is proposed and studied to understand the transmission dynamics and prevalence of HCV infection in China. Theoretical analysis indicates that the basic reproduction numberR0provides a threshold value determining whether the disease dies out or not. Two Lyapunov functions are constructed to prove the global asymptotic stability of the disease-free and the endemic equilibria, respectively. Based on data reported by the National Health and Family Planning Commission of China, the basic reproduction number is estimated as approximatelyR0=1.9897, which is much less than that for the model when a treatment strategy is not considered. An ever-increasing HCV infection is predicted in the near future. Numerical simulations, performed to investigate the potential effect of antiviral treatment, show that increasing the treatment cure rate and enlarging the treatment rate for patients at the chronic stage remain effective in reducing the number of new infections and the equilibrium prevalence. The finding suggests that treatment measures are significantly beneficial for disease control in terms of reducing new infections and, in particular, more attention should be paid to treatment for patients at the chronic stage.

PROPER PREDATION MAKES THE SYSTEM DISEASE FREE — CONCLUSION DRAWN FROM AN ECO-EPIDEMIOLOGICAL MODEL

2006 ◽  
Vol 14 (04) ◽  
pp. 599-616 ◽  
Author(s):  
SAMRAT CHATTERJEE ◽  
M. BANDYOPADHYAY ◽  
J. CHATTOPADHYAY
Keyword(s):  
Chaotic Dynamics ◽  
Chaotic Behavior ◽  
Epidemiological Model ◽  
Global Dynamics ◽  
System Parameters ◽  
System Disease ◽  
Simulation Results ◽  
Disease Free ◽  
Infected Prey ◽  
Predation Rates

In the present paper, an eco-epidemiological model consisting of susceptible prey, infected prey and predator has been proposed and analyzed. We have obtained conditions for the existence and persistence of all the three populations. To study the global dynamics of the system, numerical simulations have been performed. Our simulation results show that the system enters into quasi-periodic solutions or chaotic depending upon the choice of system parameters. To confirm the chaotic behavior of the system, we have calculated Lyapunov exponent and constructed Poincare section. Our analysis reveals that the infection and predation rates specially on the infected prey population are the key parameters that play crucial roles for controlling the chaotic dynamics of the system.

scholarly journals The Dynamics of an Eco-Epidemiological Model with Nonlinear Incidence Rate

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Raid Kamel Naji ◽  
Arkan N. Mustafa
Keyword(s):  
Incidence Rate ◽  
Dynamical Behavior ◽  
Epidemiological Model ◽  
Global Dynamics ◽  
Type Ii ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Dynamical Behaviors ◽  
Predator Model ◽  
Disease In Prey

This paper treats the dynamical behavior of eco-epidemiological model with nonlinear incidence rate. A Holling type II prey-predator model withSI-type of disease in prey has been proposed and analyzed. The existence, uniqueness, and boundedness of the solution of the system are studied. The local and global dynamical behaviors are investigated. The conditions, which guarantee the occurring of Hopf bifurcation of the system, are established. Finally, further investigations for the global dynamics of the proposed system are carried out with the help of numerical simulations.

scholarly journals Dynamical Behavior of an eco-epidemiological Model involving Disease in predator and stage structure in prey

2019 ◽  
pp. 1766-1782
Author(s):  
Lina Shihab Ahmed ◽  
Hassan Fadhil AL- Husseiny
Keyword(s):  
Steady State ◽  
Epidemic Model ◽  
Dynamical Behavior ◽  
Stage Structure ◽  
Epidemiological Model ◽  
Local Condition ◽  
Global Dynamics ◽  
Proposed Model ◽  
Disease In Predator ◽  
State Point

An eco-epidemic model is proposed in this paper. It is assumed that there is a stage structure in prey and disease in predator. Existence, uniqueness and bounded-ness of the solution for the system are studied. The existence of each possible steady state points is discussed. The local condition for stability near each steady state point is investigated. Finally, global dynamics of the proposed model is studied numerically.

GLOBAL DYNAMICS OF A DIFFERENTIAL SUSCEPTIBILITY MODEL

2012 ◽  
Vol 05 (05) ◽  
pp. 1250046
Author(s):  
M. R. RAZVAN ◽  
S. YASAMAN
Keyword(s):  
Differential Susceptibility ◽  
Index Theorem ◽  
Pitchfork Bifurcation ◽  
Epidemiological Model ◽  
Global Dynamics ◽  
Numerical Examples ◽  
Stability Properties ◽  
Hysteresis Behavior ◽  
Bifurcation Points ◽  
Susceptibility Model

An SIS epidemiological model in a population of varying size with two dissimilar groups of susceptible individuals has been analyzed. We prove that all the solutions tend to the equilibria of the system. Then we use the Poincaré Index theorem to determine the number of the rest points and their stability properties. It has been shown that bistability occurs for suitable values of the involved parameters. We use the perturbations of the pitchfork bifurcation points to give examples of all possible dynamics of the system. Some numerical examples of bistability and hysteresis behavior of the system has been also provided.

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