Modeling and simulations of a Zika virus as a mosquito-borne transmitted disease with environmental fluctuations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Chellamuthu Gokila ◽  
Muniyagounder Sambath
Keyword(s):  
Lyapunov Function ◽  
Numerical Simulations ◽  
Stationary Distribution ◽  
Zika Virus ◽  
Transmitted Disease ◽  
Threshold Value ◽  
Modeling And Simulations ◽  
Reproduction Ratio ◽  
Virus Model ◽  
Global Positive Solution

Abstract This paper deals with the stochastic Zika virus model within the human and mosquito population. Firstly, we prove that there exists a global positive solution. Further, we found the condition for a viral infection to be extinct. Besides that, we discuss the existence of a unique ergodic stationary distribution through a suitable Lyapunov function. The stationary distribution validates the occurrence of infection in the population. From that, we obtain the threshold value for prevail and disappear of disease within the population. Through the numerical simulations, we have verified the reproduction ratio R 0 S ${R}_{0}^{S}$ as stated in our theoretical findings.

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.

The quasi-stationary distribution of the closed endemic sis model

1996 ◽  
Vol 28 (3) ◽  
pp. 895-932 ◽  
Author(s):  
Ingemar Nåsell
Keyword(s):  
Stationary Distribution ◽  
Geometric Distribution ◽  
Threshold Value ◽  
Basic Reproduction Ratio ◽  
Sis Model ◽  
Reproduction Ratio ◽  
Time To Extinction ◽  
Extreme Distributions ◽  
Stochastic Sis Model ◽  
Quasi Stationary Distribution

The quasi-stationary distribution of the closed stochastic SIS model changes drastically as the basic reproduction ratio R0 passes the deterministic threshold value 1. Approximations are derived that describe these changes. The quasi-stationary distribution is approximated by a geometric distribution (discrete!) for R0 distinctly below 1 and by a normal distribution (continuous!) for R0 distinctly above 1. Uniformity of the approximation with respect to R0 allows one to study the transition between these two extreme distributions. We also study the time to extinction and the invasion and persistence thresholds of the model.

Dynamics of a stochastic rabies epidemic model with markovian switching

2021 ◽  
pp. 2150032
Author(s):  
Hao Peng ◽  
Xinhong Zhang ◽  
Daqing Jiang
Keyword(s):  
Lyapunov Function ◽  
White Noise ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Epidemic Model ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Telegraph Noise ◽  
Global Positive Solution ◽  
Theoretical Results

In this paper, we analyze a stochastic rabies epidemic model which is perturbed by both white noise and telegraph noise. First, we prove the existence of the unique global positive solution. Second, by constructing an appropriate Lyapunov function, we establish a sufficient condition for the existence of a unique ergodic stationary distribution of the positive solutions to the model. Then we establish sufficient conditions for the extinction of diseases. Finally, numerical simulations are introduced to illustrate our theoretical results.

scholarly journals Dynamical Behavior of a Stochastic SIRC Model for Influenza A

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 745 ◽  
Author(s):  
Tongqian Zhang ◽  
Tingting Ding ◽  
Ning Gao ◽  
Yi Song
Keyword(s):  
Lyapunov Function ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Epidemic Model ◽  
Influenza A ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Global Positive Solution ◽  
Theoretical Results ◽  
Stochastic Lyapunov Function

In this paper, a stochastic SIRC epidemic model for Influenza A is proposed and investigated. First, we prove that the system exists a unique global positive solution. Second, the extinction of the disease is explored and the sufficient conditions for extinction of the disease are derived. And then the existence of a unique ergodic stationary distribution of the positive solutions for the system is discussed by constructing stochastic Lyapunov function. Furthermore, numerical simulations are employed to illustrate the theoretical results. Finally, we give some further discussions about the system.

The quasi-stationary distribution of the closed endemic sis model

1996 ◽  
Vol 28 (03) ◽  
pp. 895-932 ◽  
Author(s):  
Ingemar Nåsell
Keyword(s):  
Stationary Distribution ◽  
Geometric Distribution ◽  
Threshold Value ◽  
Basic Reproduction Ratio ◽  
Sis Model ◽  
Reproduction Ratio ◽  
Time To Extinction ◽  
Extreme Distributions ◽  
Stochastic Sis Model ◽  
Quasi Stationary Distribution

The quasi-stationary distribution of the closed stochastic SIS model changes drastically as the basic reproduction ratio R 0 passes the deterministic threshold value 1. Approximations are derived that describe these changes. The quasi-stationary distribution is approximated by a geometric distribution (discrete!) for R 0 distinctly below 1 and by a normal distribution (continuous!) for R 0 distinctly above 1. Uniformity of the approximation with respect to R 0 allows one to study the transition between these two extreme distributions. We also study the time to extinction and the invasion and persistence thresholds of the model.

scholarly journals Stationary distribution of a stochastic SIRD epidemic model of Ebola with double saturated incidence rates and vaccination

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Panpan Wang ◽  
Jianwen Jia
Keyword(s):  
Stochastic Model ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Stationary Distribution ◽  
Epidemic Model ◽  
Existence And Uniqueness ◽  
Lyapunov Functions ◽  
Incidence Rates ◽  
Saturated Incidence ◽  
Global Positive Solution

Abstract In this paper, a stochastic SIRD model of Ebola with double saturated incidence rates and vaccination is considered. Firstly, the existence and uniqueness of a global positive solution are obtained. Secondly, by constructing suitable Lyapunov functions and using Khasminskii’s theory, we show that the stochastic model has a unique stationary distribution. Moreover, the extinction of the disease is also analyzed. Finally, numerical simulations are carried out to portray the analytical results.

Analysis on stochastic predator-prey model with distributed delay

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
C. Gokila ◽  
M. Sambath
Keyword(s):  
Lyapunov Function ◽  
Numerical Simulations ◽  
Stationary Distribution ◽  
Sufficient Conditions ◽  
Distributed Delay ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Disease In Prey ◽  
Stochastic Lyapunov Function

Abstract In the present work, we consider a stochastic predator-prey model with disease in prey and distributed delay. Firstly, we establish sufficient conditions for the extinction of the disease and also permanence of healthy prey and predator. Besides, we obtain the condition for the existence of an ergodic stationary distribution through the stochastic Lyapunov function. Finally, we provide some numerical simulations to validate our theoretical findings.

scholarly journals Dynamics of a Stochastic Three-Species Food Web Model with Omnivory and Ratio-Dependent Functional Response

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-19
Author(s):  
Guirong Liu ◽  
Rong Liu
Keyword(s):  
Lyapunov Function ◽  
Numerical Simulations ◽  
Food Web ◽  
Positive Solution ◽  
Sufficient Conditions ◽  
Stochastic Comparison ◽  
Top Predator ◽  
Global Positive Solution ◽  
Persistent In Mean ◽  
Food Web Model

This paper is concerned with a stochastic three-species food web model with omnivory which is defined as feeding on more than one trophic level. The model involves a prey, an intermediate predator, and an omnivorous top predator. First, by the stochastic comparison theorem, we show that there is a unique global positive solution to the model. Next, we investigate the asymptotic pathwise behavior of the model. Then, we conclude that the model is persistent in mean and extinct and discuss the stochastic persistence of the model. Further, by constructing a suitable Lyapunov function, we establish sufficient conditions for the existence of an ergodic stationary distribution to the model. Then, we present the application of the main results in some special models. Finally, we introduce some numerical simulations to support the main results obtained. The results in this paper generalize and improve the previous related results.

scholarly journals Ergodic Stationary Distribution of a Stochastic Hepatitis B Epidemic Model with Interval-Valued Parameters and Compensated Poisson Process

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Driss Kiouach ◽  
Yassine Sabbar
Keyword(s):  
Hepatitis B ◽  
Poisson Process ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Stationary Distribution ◽  
Epidemic Model ◽  
Environmental Disturbances ◽  
Analytical Results ◽  
Global Positive Solution ◽  
Interval Valued

Hepatitis B epidemic was and is still a rich subject that sparks the interest of epidemiological researchers. The dynamics of this epidemic is often modeled by a system with constant parameters. In reality, the parameters associated with the Hepatitis B model are not certain, but the interval in which it belongs to can readily be determined. Our paper focuses on an imprecise Hepatitis B model perturbed by Lévy noise due to unexpected environmental disturbances. This model has a global positive solution. Under an appropriate assumption, we prove the existence of a unique ergodic stationary distribution by using the mutually exclusive possibilities lemma demonstrated by Stettner in 1986. Our main effort is to establish an almost perfect condition for the existence of the stationary distribution. Numerical simulations are introduced to illustrate the analytical results.

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