scholarly journals Dynamics of a stochastic COVID-19 epidemic model with jump-diffusion

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Almaz Tesfay ◽  
Tareq Saeed ◽  
Anwar Zeb ◽  
Daniel Tesfay ◽  
Anas Khalaf ◽  
...  
Keyword(s):  
Stochastic Model ◽  
Existence And Uniqueness ◽  
Numerical Experiments ◽  
Random Perturbation ◽  
Jump Diffusion ◽  
Disease Outbreak ◽  
Stochastic Noises ◽  
Stochastic Epidemic ◽  
Global Positive Solution ◽  
The Impact

AbstractFor a stochastic COVID-19 model with jump-diffusion, we prove the existence and uniqueness of the global positive solution. We also investigate some conditions for the extinction and persistence of the disease. We calculate the threshold of the stochastic epidemic system which determines the extinction or permanence of the disease at different intensities of the stochastic noises. This threshold is denoted by ξ which depends on white and jump noises. The effects of these noises on the dynamics of the model are studied. The numerical experiments show that the random perturbation introduced in the stochastic model suppresses disease outbreak as compared to its deterministic counterpart. In other words, the impact of the noises on the extinction and persistence is high. When the noise is large or small, our numerical findings show that COVID-19 vanishes from the population if $\xi <1$ ξ < 1 ; whereas the epidemic cannot go out of control if $\xi >1$ ξ > 1 . From this, we observe that white noise and jump noise have a significant effect on the spread of COVID-19 infection, i.e., we can conclude that the stochastic model is more realistic than the deterministic one. Finally, to illustrate this phenomenon, we put some numerical simulations.

scholarly journals Stochastic Modeling for HIV and AIDS Epidemics With Viral Load Detectability

2020 ◽  
Vol 9 (4) ◽  
pp. 33
Author(s):  
Peter Emeda Tengaa ◽  
Samuel Mwalili ◽  
George Otieno Orwa
Keyword(s):  
Viral Load ◽  
Stochastic Model ◽  
Existence And Uniqueness ◽  
Reproduction Number ◽  
Control Strategies ◽  
Random Perturbation ◽  
Disease Outbreak ◽  
Hiv And Aids ◽  
Persistence Properties ◽  
Stochastic Epidemic

In this paper, we investigated on the stochastic epidemic model by incorporating viral load detectability. We derived HIV and AIDS stochastic model from the deterministic counterpart model and presented a stochastic threshold in terms of stochastic basic reproduction number. We showed that R_s^0 &lt; 1 then the disease dies out exponentially and when R_s^0 &gt; 1 the disease persists in the population. We further derived the existence and uniqueness, extinction and persistence properties of the stochastic model models, then the numerical simulation is done by using Milsten&rsquo;s numerical scheme. The finding shows that the random perturbation introduced in the stochastic model suppresses disease outbreak as compared to its deterministic counterparts which provide some useful control strategies to eradicate the disease

scholarly journals On stability of stochastic delay model for tumor-immune interaction

Filomat ◽  
2018 ◽  
Vol 32 (4) ◽  
pp. 1273-1283
Author(s):  
Marija Krstic
Keyword(s):  
Stochastic Model ◽  
Existence And Uniqueness ◽  
Interaction Model ◽  
Reliable Data ◽  
Lyapunov Functionals ◽  
Resting Cells ◽  
Random Perturbations ◽  
Delay Model ◽  
Stochastic Delay ◽  
Global Positive Solution

In this paper we study a stochastic model for tumor-immune interaction with delay. More precisely, we extend the deterministic delay tumor-immune interaction model by introducing random perturbations and obtain stochastic model. For this model, we first prove existence and uniqueness of the global positive solution, and then, by using suitable Lyapunov functionals, we obtain stability conditions for the equilibrium state when tumor cells and resting cells approach their carrying capacities. We also carry numerical simulation with reliable data to illustrate our theoretical findings.

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.

scholarly journals Global Analysis of a Novel Nonlinear Stochastic SIVS Epidemic System with Vaccination Control

2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
Xiaona Leng ◽  
Tao Feng ◽  
Xinzhu Meng
Keyword(s):  
Numerical Simulations ◽  
Existence And Uniqueness ◽  
Stochastic Dynamics ◽  
Global Analysis ◽  
Lyapunov Methods ◽  
Stochastic Disturbances ◽  
Epidemic Disease ◽  
Stochastic Noises ◽  
Global Positive Solution ◽  
Epidemic Diseases

This paper proposes a stochastic SIVS epidemic system with nonlinear saturated infection rate under vaccination and investigates the dynamics predicted by the model. By using Itô’s formula and Lyapunov methods, we first study the existence and uniqueness of global positive solution. Then we investigate the stochastic dynamics of the system and obtain the thresholds which govern the extinction and the spread of the epidemic disease. Results show that large stochastic noises can lead to the extinction of epidemic diseases; that is, stochastic disturbances can suppress the outbreak of epidemic diseases. Finally, we carry out a series of numerical simulations to demonstrate the performance of our theoretical findings.

scholarly journals Correlated Stochastic Epidemic Model for the Dynamics of SARS-CoV-2 with Vaccination

2021 ◽  
Author(s):  
Tahir Khan ◽  
Roman Ullah ◽  
Gul Zaman ◽  
Youssef Khatib
Keyword(s):  
Mathematical Model ◽  
Brownian Motion ◽  
Stochastic Model ◽  
Existence And Uniqueness ◽  
Human Population ◽  
Sufficient Conditions ◽  
Stochastic Epidemic ◽  
Stochastic Epidemic Model ◽  
Virus Spreading ◽  
Theoretical Results

Abstract We formulate a mathematical model has been proposed to describe the stochastic influence of SARS-CoV-2 virus with various sources of randomness and vaccination. We assume the various sources of ran-domness in each population groups by different Brownian motion. We develop the correlated stochastic model by taking into account the various sources of randomness by different Brownian motions and distributed the total human population in three groups of susceptible, infected and recovered with reservoir class. Because reservoir play a significant role in the transmission of SARS-CoV-2 virus spreading. Moreover, the vaccination of susceptible are also accorded. Once we formulate the correlated stochastic model, the existence and uniqueness of positive solution will be discussed to show the problem feasibility. The SARS-CoV-2 extinction as well as persistency will be also discussed and we will obtain the sufficient conditions for it. At the last all the theoretical results will be supported via numerical/graphical findings.

scholarly journals Valuation of Insurance Products with Shout Options in a Jump-Diffusion Model

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Jun Liu ◽  
Zhian Liang
Keyword(s):  
Diffusion Model ◽  
Differential Inequality ◽  
Sharp Increase ◽  
Numerical Experiments ◽  
Jump Diffusion ◽  
Underlying Asset ◽  
Put Options ◽  
Insurance Product ◽  
Jump Diffusion Model ◽  
The Impact

The insurance product with shout options which permit the holders to modify the contract rules is one of the most popular products in European and American markets today. Therefore, it is of great significance to price more precisely. A new mathematical model consisting of a partial differential inequality and constraint conditions is derived for the price of insurance products in a jump-diffusion model. The numerical experiments are performed to analyze the impact of parameters on the insurance product with shout put options, especially for the jump times and the quantities of shout opportunities. The experiment results show that the value of the product is strongly affected by the quantities of shouting opportunities, especially for high values of the underlying asset, while it is only weakly affected for low values. Meanwhile, another meaningful discovery is that the valuation has changed little as the jump times are less than five, while it has shown a sharp increase once the jump times are more than five. Furthermore, the indicator results of course grid errors show that the values of shout put options in the jump-diffusion model are more accurate than those in a Brownian motion.

scholarly journals A SIRS Epidemic Model Incorporating Media Coverage with Random Perturbation

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Wenbin Liu
Keyword(s):  
Stochastic Model ◽  
Epidemic Model ◽  
Media Coverage ◽  
Complex Dynamics ◽  
Deterministic Model ◽  
Random Perturbation ◽  
Endemic Equilibrium ◽  
Sirs Epidemic Model ◽  
Stochastic Epidemic ◽  
The Stability

We investigate the complex dynamics of a SIRS epidemic model incorporating media coverage with random perturbation. We first deal with the boundedness and the stability of the disease—free and endemic equilibria of the deterministic model. And for the corresponding stochastic epidemic model, we prove that the endemic equilibrium of the stochastic model is asymptotically stable in the large. Furthermore, we perform some numerical examples to validate the analytical finding, and find that if the conditions of stochastic stability are not satisfied, the solution for the stochastic model will oscillate strongly around the endemic equilibrium.

scholarly journals Dynamical Analysis of Two-Microorganism and Single Nutrient Stochastic Chemostat Model with Monod-Haldane Response Function

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Mengnan Chi ◽  
Wencai Zhao
Keyword(s):  
Lyapunov Function ◽  
Response Function ◽  
Existence And Uniqueness ◽  
Random Perturbation ◽  
Equilibrium Points ◽  
Dynamical Analysis ◽  
Deterministic System ◽  
Chemostat Model ◽  
Global Positive Solution ◽  
The Stability

In this paper, we formulate and investigate a two-microorganism and single nutrient chemostat model with Monod-Haldane response function and random perturbation. First, for the corresponding deterministic system, we introduce the conditions of the stability of the equilibrium points. Then, using Lyapunov function and Itô’s formula, we investigate the existence and uniqueness of the global positive solution of the stochastic chemostat model. Furthermore, we explore and obtain the criterions of the extinction and the permanence for the stochastic model. Finally, numerical simulations are carried out to illustrate our main results.

scholarly journals Empirical Stochastic Model of Multi-GNSS Measurements

Sensors ◽  
2021 ◽  
Vol 21 (13) ◽  
pp. 4566
Author(s):  
Dominik Prochniewicz ◽  
Kinga Wezka ◽  
Joanna Kozuchowska
Keyword(s):  
Stochastic Model ◽  
Density Ratio ◽  
Functional Model ◽  
Optimal Solution ◽  
Global Navigation Satellite Systems ◽  
Unknown Parameters ◽  
Short Baseline ◽  
Stochastic Parameters ◽  
Dependent Model ◽  
The Impact

The stochastic model, together with the functional model, form the mathematical model of observation that enables the estimation of the unknown parameters. In Global Navigation Satellite Systems (GNSS), the stochastic model is an especially important element as it affects not only the accuracy of the positioning model solution, but also the reliability of the carrier-phase ambiguity resolution (AR). In this paper, we study in detail the stochastic modeling problem for Multi-GNSS positioning models, for which the standard approach used so far was to adopt stochastic parameters from the Global Positioning System (GPS). The aim of this work is to develop an individual, empirical stochastic model for each signal and each satellite block for GPS, GLONASS, Galileo and BeiDou systems. The realistic stochastic model is created in the form of a fully populated variance-covariance (VC) matrix that takes into account, in addition to the Carrier-to-Noise density Ratio (C/N0)-dependent variance function, also the cross- and time-correlations between the observations. The weekly measurements from a zero-length and very short baseline are utilized to derive stochastic parameters. The impact on the AR and solution accuracy is analyzed for different positioning scenarios using the modified Kalman Filter. Comparing the positioning results obtained for the created model with respect to the results for the standard elevation-dependent model allows to conclude that the individual empirical stochastic model increases the accuracy of positioning solution and the efficiency of AR. The optimal solution is achieved for four-system Multi-GNSS solution using fully populated empirical model individual for satellite blocks, which provides a 2% increase in the effectiveness of the AR (up to 100%), an increase in the number of solutions with errors below 5 mm by 37% and a reduction in the maximum error by 6 mm compared to the Multi-GNSS solution using the elevation-dependent model with neglected measurements correlations.

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