scholarly journals Ergodic Stationary Distribution of Hepatitis C Virus Model Incorporating Two Treatment Effects

2021 ◽  
Author(s):  
Auwal Abdullahi
Keyword(s):  
Hepatitis C ◽  
Stationary Distribution ◽  
Treatment Effects ◽  
Disease Model ◽  
Sufficient Conditions ◽  
Treatment Rate ◽  
Lyapunov Approach ◽  
Infectious Disease Model ◽  
Virus Model ◽  
Stochastic Properties

In this paper, the dynamics of Hepatitis C infectious disease model with two treatment effects are studied through the Ito Stochastic Differential Equations (SDEs). While the first treatment rate reduces the reproduction of virion, the other mitigates the new infections. Though the deterministic behaviour of the model has been extensively studied, little is known about its stochastic properties. Thus, we examine sufficient conditions for the existence and uniqueness of the ergodic stationary distribution of the model via stochastic Lyapunov approach. The existence of a unique positive solution is also studied. The numerical simulations of the SDE model are performed through the Euler-Maruyama method and compared with their deterministic counterparts. The results obtained by SDEs are found to conform to those reported through their deterministic analogues.

scholarly journals Threshold Analysis and Stationary Distribution of a Stochastic Model with Relapse and Temporary Immunity

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 331 ◽  
Author(s):  
Peng Liu ◽  
Xinzhu Meng ◽  
Haokun Qi
Keyword(s):  
Stochastic Model ◽  
Stationary Distribution ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Markov Semigroup ◽  
Threshold Analysis ◽  
Numerical Examples ◽  
Stochastic Properties ◽  
Symmetric Method ◽  
Temporary Immunity

In this paper, a stochastic model with relapse and temporary immunity is formulated. The main purpose of this model is to investigate the stochastic properties. For two incidence rate terms, we apply the ideas of a symmetric method to obtain the results. First, by constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the extinction and persistence of this system. Then, we investigate the existence of a stationary distribution for this model by employing the theory of an integral Markov semigroup. Finally, the numerical examples are presented to illustrate the analytical findings.

Stability and Bifurcation Analysis of a Stage-Structured SIR Model with Time Delays

2012 ◽  
Vol 468-471 ◽  
pp. 1070-1073
Author(s):  
Shan Wen Yan ◽  
Li Zhang
Keyword(s):  
Infectious Disease ◽  
Time Delays ◽  
Disease Model ◽  
Sufficient Conditions ◽  
Sir Model ◽  
Constant Time Delay ◽  
Infectious Disease Model ◽  
Stability And Bifurcation Analysis ◽  
The Stability ◽  
Two Stages

In this paper, we considered a SIR infectious disease model with two stages, immature and mature, with the time to maturity represented by a constant time delay. Positivity and boundness of solutions and sufficient conditions of the stability of equilibria are obtained.

Normal approximations to discrete unimodal distributions

1986 ◽  
Vol 23 (04) ◽  
pp. 1013-1018
Author(s):  
B. G. Quinn ◽  
H. L. MacGillivray
Keyword(s):  
Stationary Distribution ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Hypergeometric Distribution ◽  
Death Process ◽  
Normal Approximations ◽  
Discrete Random Variables ◽  
Birth Death

Sufficient conditions are presented for the limiting normality of sequences of discrete random variables possessing unimodal distributions. The conditions are applied to obtain normal approximations directly for the hypergeometric distribution and the stationary distribution of a special birth-death process.

Approximating the stationary distribution of an infinite stochastic matrix

1991 ◽  
Vol 28 (1) ◽  
pp. 96-103 ◽  
Author(s):  
Daniel P. Heyman
Keyword(s):  
Markov Chain ◽  
Steady State ◽  
Stationary Distribution ◽  
Numerical Approximation ◽  
Stochastic Matrix ◽  
Sufficient Conditions ◽  
Finite System ◽  
Balance Equations ◽  
The Given ◽  
Steady State Balance

We are given a Markov chain with states 0, 1, 2, ···. We want to get a numerical approximation of the steady-state balance equations. To do this, we truncate the chain, keeping the first n states, make the resulting matrix stochastic in some convenient way, and solve the finite system. The purpose of this paper is to provide some sufficient conditions that imply that as n tends to infinity, the stationary distributions of the truncated chains converge to the stationary distribution of the given chain. Our approach is completely probabilistic, and our conditions are given in probabilistic terms. We illustrate how to verify these conditions with five examples.

The threshold for a stochastic within-host CHIKV virus model with saturated incidence rate

2021 ◽  
pp. 2150042
Author(s):  
C. Gokila ◽  
M. Sambath
Keyword(s):  
Lyapunov Function ◽  
Incidence Rate ◽  
Stationary Distribution ◽  
Reproduction Number ◽  
Threshold Value ◽  
Saturated Incidence Rate ◽  
Number Formula ◽  
Saturated Incidence ◽  
Virus Model ◽  
Global Positive Solution

This paper deals with stochastic Chikungunya (CHIKV) virus model along with saturated incidence rate. We show that there exists a unique global positive solution and also we obtain the conditions for the disease to be extinct. We also discuss about the existence of a unique ergodic stationary distribution of the model, through a suitable Lyapunov function. The stationary distribution validates the occurrence of disease; through that, we find the threshold value for prevail and disappear of disease within host. With the help of numerical simulations, we validate the stochastic reproduction number [Formula: see text] as stated in our theoretical findings.

scholarly journals Obesity as an "infectious" disease

2021 ◽  
Vol 11 (9) ◽  
pp. 534-537
Author(s):  
Daria Żuraw ◽  
Paulina Oleksa ◽  
Mateusz Sobczyk
Keyword(s):  
Infectious Disease ◽  
Disease Model ◽  
Living Environment ◽  
Social Contagion ◽  
Social Discrimination ◽  
Obese People ◽  
Obesity Epidemic ◽  
Global Epidemic ◽  
Infectious Disease Model ◽  
The One

Introduction: Obesity has been recognized as a global epidemic by the WHO, followed by a wealth of empirical evidence supporting its contagiousness. However, the dynamics of the spread of obesity between individuals are rarely studied.  A distinguishing feature of the obesity epidemic is that it is driven by a process of social contagion that cannot be perfectly described by the infectious disease model. There is also social discrimination in the obesity epidemic. Social discrimination against obese people plays quite different roles in two cases: on the one hand, when obesity cannot be eliminated, social discrimination can reduce the number of obese people; on the other hand, when obesity is eradicable, social discrimination can cause it to explode.(1)   Materiał and methods: A literature analysis on obesity epidemic was carried out within the Pubmed, Google scholar and Research Gate platform. The following keywords were used in serach: obesity, epidemy, children, body max index.    Purpose of the work: The aim of the following analysis is to present an obesity as an infectious disease. The steadily increasing percentage of obese people, including children, shows that there is an obesity epidemic. This is the phenomenon of social contagion, which partially explains the concept of homophily, which involves the grouping of people with similar characteristics. Potential explanations are also provided by sharing a living environment with similar access to certain foods and similar opportunities for physical activity, which defines the occurrence of analogous health habits

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