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 Stationary Distribution and Extinction of a Stochastic SIQR Model with Saturated Incidence Rate

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Qiuhua Zhang ◽  
Kai Zhou
Keyword(s):  
Lyapunov Function ◽  
Incidence Rate ◽  
Stationary Distribution ◽  
Epidemic Model ◽  
Existence And Uniqueness ◽  
Sufficient Condition ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
Dynamical Properties ◽  
Theoretical Results

In this paper, we consider a stochastic SIQR epidemic model with saturated incidence rate. By constructing a proper Lyapunov function, we obtain the existence and uniqueness of positive solution for this SIQR model. Furthermore, we study the dynamical properties of this stochastic SIQR model; that is, (i) we establish the sufficient condition for the existence of ergodic stationary distribution of the model; (ii) we obtain the extinction of the disease under some conditions. At last, numerical simulations are introduced to illustrate our theoretical results.

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 dynamics of a delayed deterministic and stochastic epidemic SIR models with a saturated incidence rate

2018 ◽  
Vol 26 (4) ◽  
pp. 235-245 ◽  
Author(s):  
Modeste N’zi ◽  
Ilimidi Yattara
Keyword(s):  
Stochastic Model ◽  
White Noise ◽  
Incidence Rate ◽  
Deterministic Model ◽  
Contact Rate ◽  
Almost Sure Stability ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
Global Positive Solution ◽  
Disease Free

AbstractWe treat a delayed SIR (susceptible, infected, recovered) epidemic model with a saturated incidence rate and its perturbation through the contact rate using a white noise. We start with a deterministic model and then add a perturbation on the contact rate using a white noise to obtain a stochastic model. We prove the existence and uniqueness of the global positive solution for both deterministic and stochastic delayed differential equations. Under suitable conditions on the parameters, we study the global asymptotic stability of the disease-free equilibrium of the deterministic model and the almost sure stability of the disease-free equilibrium of the stochastic model.

scholarly journals Stability analysis in a delayed SIR epidemic model with a saturated incidence rate

2010 ◽  
Vol 15 (3) ◽  
pp. 299-306 ◽  
Author(s):  
A. Kaddar
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Asymptotically Stable ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
The Basic Reproduction Number

We formulate a delayed SIR epidemic model by introducing a latent period into susceptible, and infectious individuals in incidence rate. This new reformulation provides a reasonable role of incubation period on the dynamics of SIR epidemic model. We show that if the basic reproduction number, denoted, R0, is less than unity, the diseasefree equilibrium is locally asymptotically stable. Moreover, we prove that if R0 > 1, the endemic equilibrium is locally asymptotically stable. In the end some numerical simulations are given to compare our model with existing model.

Dynamical behavior of a stochastic multigroup staged-progression HIV model with saturated incidence rate and higher-order perturbations

2021 ◽  
pp. 2150051
Author(s):  
Qun Liu ◽  
Daqing Jiang
Keyword(s):  
Incidence Rate ◽  
Stationary Distribution ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Hiv Model ◽  
Progression Model ◽  
Saturated Incidence Rate ◽  
Biological Interpretation ◽  
Saturated Incidence

In this paper, we analyze a higher-order stochastically perturbed multigroup staged-progression model for the transmission of HIV with saturated incidence rate. We obtain sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of positive solutions to the system by establishing a suitable stochastic Lyapunov function. In addition, we make up adequate conditions for complete eradication and wiping out the infectious disease. In a biological interpretation, the existence of a stationary distribution implies that the disease will prevail and persist in the long term. Finally, examples and numerical simulations are introduced to validate our theoretical results.

scholarly journals Mathematical Modelling and Analysis of Dengue Transmission in Bangladesh with Saturated Incidence Rate and Constant Treatment Function

2021 ◽  
Vol 3 (2) ◽  
pp. 101-113
Author(s):  
Amit Kumar Chakraborty ◽  
M. A. Haque ◽  
M. A. Islam
Keyword(s):  
Incidence Rate ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Human Populations ◽  
Vector Population ◽  
Sirs Model ◽  
Treatment Function ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
The Stability

Dengue is one of the major health problems in Bangladesh and many people are died in recent years due to the severity of this disease. Therefore, in this paper, a SIRS model for the human and SI model for vector population with saturated incidence rate and constant treatment function has been presented to describe the transmission of dengue. The equilibrium points and the basic reproduction number have been computed. The conditions which lead the disease free equilibrium and the endemic equilibrium have been determined. The local stability for the equilibrium points has been established based on the eigenvalues of the Jacobian matrix and the global stability has been analyzed by using the Lyapunov function theory. It is found that the stability of equilibrium points can be controlled by the reproduction number. In order to calculate the infection rate, data for infected human populations have been collected from several health institutions of Bangladesh. Numerical simulations of various compartments have been generated using MATLAB to investigate the influence of the key parameters for the transmission of the disease and to support the analytical results. The effect of treatment function over the infected compartment has been illustrated. The sensitivity of the reproduction number concerning the parameters of the model has been analyzed. Finally, the most sensitive parameter that has the highest effect over reproduction number has been identified.

scholarly journals Study of Dynamics of a COVID-19 Model for Saudi Arabia with Vaccination Rate, Saturated Treatment Function and Saturated Incidence Rate

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3134
Author(s):  
Rubayyi T. Alqahtani ◽  
Abdelhamid Ajbar
Keyword(s):  
Saudi Arabia ◽  
Incidence Rate ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Arab World ◽  
Vaccination Rate ◽  
Treatment Function ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
The Basic Reproduction Number

This paper proposes, validates and analyzes the dynamics of the susceptible exposed infectious recovered (SEIR) model for the propagation of COVID-19 in Saudi Arabia, which recorded the largest number of cases in the Arab world. The model incorporates a saturated incidence rate, a constant vaccination rate and a nonlinear treatment function. The rate of treatment is assumed to be proportional to the number of infected persons when this number is low and reaches a fixed value for large number of infected individuals. The expression of the basic reproduction number is derived, and the model basic stability properties are studied. We show that when the basic reproduction number is less than one the model can predict both a Hopf and backward bifurcations. Simulations are also provided to fit the model to COVID-19 data in Saudi Arabia and to study the effects of the parameters of the treatment function and vaccination rate on disease control.

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