scholarly journals On dynamics of fractional incommensurate model of Covid-19 with nonlinear saturated incidence rate

2021 ◽  
Author(s):  
Abdelouahed ALLA HAMOU ◽  
ELHOUSSINE AZROUL ◽  
Zakia Hammouch ◽  
Abdelilah Lamrani alaoui
Keyword(s):  
Incidence Rate ◽  
Least Squares Method ◽  
Real Data ◽  
Euler Method ◽  
Proposed Model ◽  
The World ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
Fractional Orders ◽  
Theoretical Results

In December 2019, a new virus belonging to the coronavirus strain has been discovered in Wuhan, China, this virus has attracted world-wide attention and it spread rapidly in the world, reaching nearly 216 countries in the world in November 2020. In this chapter, we study the fractional incommensurate SIQR (susceptible, infections, quarantined and removed) COVID-19 model with nonlinear saturated incidence rate using Atangana-Baleanu fractional derivatives. The existence and uniqueness of the solutions for the fractional model is proved using fixed point theorem, the model are shown to have two equilibrium point (disease free and an endemic equilibrium). Some numerical simulations using Euler method are also carried out to support our theoretical results. We estimated the value of the fractional orders and the parameters of the proposed model using the least squares method. Further, the sensitivity analysis of the parameter is performed as a result, our incommensurate model gives a good approximation to real data of COVID-19.

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.

Mathematical modeling approach to the transmission dynamics of pine wilt disease with saturated incidence rate

2018 ◽  
Vol 11 (03) ◽  
pp. 1850035 ◽  
Author(s):  
Muhammad Altaf Khan ◽  
Kamil Shah ◽  
Yasir Khan ◽  
Saeed Islam
Keyword(s):  
Incidence Rate ◽  
Local Stability ◽  
Pine Wilt Disease ◽  
Wilt Disease ◽  
Pine Wilt ◽  
Proposed Model ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
Disease Free ◽  
Endemic State

The present paper investigates the dynamics of pine wilt disease with saturated incidence rate. The proposed model is stable both locally and globally. The local stability of the disease-free equilibrium is determined by the basic reproduction [Formula: see text]. The disease-free equilibrium is stable locally and globally whenever [Formula: see text]. If [Formula: see text], then the endemic state is stable both locally and globally. Further, a brief discussion with conclusion on the numerical results of the proposed model is presented.

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 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 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

Simulation of consumers decision-making process using agent-based model approach

2019 ◽  
Vol 10 (06) ◽  
pp. 1950037
Author(s):  
Daniel Soto Forero ◽  
Yony F. Ceballos ◽  
German Sànchez Torres
Keyword(s):  
Decision Making ◽  
Fuzzy Logic ◽  
Real Data ◽  
World Market ◽  
Decision Making Process ◽  
Agent Based ◽  
Dynamic Social Network ◽  
Proposed Model ◽  
The World ◽  
Model Approach

This paper describes a model to simulate the decision-making process of consumers that adopts technology within a dynamic social network. The proposed model use theories and tools from the psychology of consumer behavior, social networks and complex dynamical systems like the Consumat framework and fuzzy logic. The model has been adjusted using real data, tested with the automobile market and it can recreate trends like those described in the world market.

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