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.

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 Mathematical Analysis and Stochastic Stability of Nonlinear Epidemic Model with Incidence Rate

2020 ◽  
pp. 8-19
Author(s):  
Laid Chahrazed
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Globally Asymptotically Stable ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
The Stability ◽  
Disease Free ◽  
Temporary Immunity

In this work, we consider a nonlinear epidemic model with temporary immunity and saturated incidence rate. Size N(t) at time t, is divided into three sub classes, with N(t)=S(t)+I(t)+Q(t); where S(t), I(t) and Q(t) denote the sizes of the population susceptible to disease, infectious and quarantine members with the possibility of infection through temporary immunity, respectively. We have made the following contributions: The local stabilities of the infection-free equilibrium and endemic equilibrium are; analyzed, respectively. The stability of a disease-free equilibrium and the existence of other nontrivial equilibria can be determine by the ratio called the basic reproductive number, This paper study the reduce model with replace S with N, which does not have non-trivial periodic orbits with conditions. The endemic -disease point is globally asymptotically stable if R0 ˃1; and study some proprieties of equilibrium with theorems under some conditions. Finally the stochastic stabilities with the proof of some theorems. In this work, we have used the different references cited in different studies and especially the writing of the non-linear epidemic mathematical model with [1-7]. We have used the other references for the study the different stability and other sections with [8-26]; and sometimes the previous references.

Dynamical Analysis of Salmonella Epidemic Model With Saturated Incidence Rate

2021 ◽  
pp. 545-560
Author(s):  
Abiodun Oluwakemi ◽  
Ibrahim Mohammed ◽  
Adebimpe Olukayode ◽  
Oludoun Olajumoke ◽  
Gbadamosi Babatunde ◽  
...  
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Dynamical Analysis ◽  
Saturated Incidence Rate ◽  
Saturated Incidence

Stability analysis of an SVIR epidemic model with non-linear saturated incidence rate

2015 ◽  
Vol 9 ◽  
pp. 1145-1158
Author(s):  
Muhammad Altaf Khan ◽  
Zulfiqar Ali ◽  
L. C. C. Dennis ◽  
Ilyas Khan ◽  
Saeed Islam ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Incidence Rate ◽  
Epidemic Model ◽  
Non Linear ◽  
Saturated Incidence Rate ◽  
Saturated Incidence

Deterministic and stochastic stability of an SIRS epidemic model with a saturated incidence rate

2017 ◽  
Vol 25 (1) ◽  
Author(s):  
Modeste N’zi ◽  
Jacques Tano
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Deterministic Model ◽  
Random Noise ◽  
Stochastic Version ◽  
Noise Perturbation ◽  
Sirs Epidemic Model ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
Disease Free

AbstractIn this paper, we formulate an epidemic model for the spread of an infectious disease in a population of varying size. The total population is divided into three distinct epidemiological subclass of individuals (susceptible, infectious and recovered) and we study a deterministic and stochastic models with saturated incidence rate. The stochastic model is obtained by incorporating a random noise into the deterministic model. In the deterministic case, we briefly discuss the global asymptotic stability of the disease free equilibrium by using a Lyapunov function. For the stochastic version, we study the global existence and positivity of the solution. Under suitable conditions on the intensity of the white noise perturbation, we prove that there are a

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