Numerical treatment of stochastic heroin epidemic model

Abstract We have presented the numerical analysis of a stochastic heroin epidemic model in this paper. The mean of stochastic heroin model is itself a deterministic solution. The effect of reproduction number has also been observed in the stochastic heroin epidemic model. We have developed some stochastic explicit and implicitly driven explicit methods for this model. But stochastic explicit methods have flopped for certain values of parameters. In support, some theorems and graphical illustrations are presented.

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Analysis of a Diffusive Heroin Epidemic Model in a Heterogeneous Environment

Complexity ◽

10.1155/2020/8268950 ◽

2020 ◽

Vol 2020 ◽

pp. 1-12

Author(s):

Jinliang Wang ◽

Hongquan Sun

Keyword(s):

Steady State ◽

Basic Reproduction Number ◽

Epidemic Model ◽

Reproduction Number ◽

Reaction Diffusion ◽

Threshold Dynamics ◽

Heterogeneous Environment ◽

Threshold Parameter ◽

Simulation Results ◽

Heroin Model

This paper is concerned with a reaction-diffusion heroin model in a bound domain. The objective of this paper is to explore the threshold dynamics based on threshold parameter and basic reproduction number (BRN) ℜ0, and it is proved that if ℜ0<1, heroin spread will be extinct, while if ℜ0>1, heroin spread is uniformly persistent and there exists a positive heroin-spread steady state. We also obtain that the explicit formula of ℜ0 and global attractiveness of constant positive steady state (PSS) when all parameters are positive constants. Our simulation results reveal that compared to the homogeneous setting, the spatial heterogeneity has essential impacts on increasing the risk of heroin spread.

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An SIS epidemic model with time delay and stochastic perturbation on heterogeneous networks

Mathematical Biosciences and Engineering ◽

10.3934/mbe.2021337 ◽

2021 ◽

Vol 18 (5) ◽

pp. 6790-6805

Author(s):

Meici Sun ◽

◽

Qiming Liu

Keyword(s):

Time Delay ◽

Epidemic Model ◽

Deterministic Model ◽

Reproduction Number ◽

Sufficient Conditions ◽

Stochastic Perturbation ◽

Scale Free ◽

Sis Epidemic Model ◽

The Mean ◽

Sis Epidemic

<abstract><p>An SIS epidemic model with time delay and stochastic perturbation on scale-free networks is established in this paper. And we derive sufficient conditions guaranteeing extinction and persistence of epidemics, respectively, which are related to the basic reproduction number $ R_0 $ of the corresponding deterministic model. When $ R_0 < 1 $, almost surely exponential extinction and $ p $-th moment exponential extinction of epidemics are proved by Razumikhin-Mao Theorem. Whereas, when $ R_0 > 1 $, the system is persistent in the mean under sufficiently weak noise intensities, which indicates that the disease will prevail. Finally, the main results are demonstrated by numerical simulations.</p></abstract>

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Stability Analysis of an SEIR Epidemic Model with Stochastic Perturbation and Numerical Simulation

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2012-0054 ◽

2013 ◽

Vol 14 (2) ◽

Cited By ~ 4

Author(s):

Xiaoming Fan ◽

Zhigang Wang

Keyword(s):

Numerical Simulation ◽

Asymptotic Behavior ◽

Epidemic Model ◽

Reproduction Number ◽

Stochastic Perturbation ◽

Random Fluctuation ◽

Deterministic System ◽

Stochastic Version ◽

Special Case ◽

The Basic Reproduction Number

AbstractAn SEIR epidemic model with constant immigration and random fluctuation around the endemic equilibrium is considered. As a special case, a deterministic system discussed by Li et al. will be incorporated into the stochastic version given by us. We carry out a detailed analysis on the asymptotic behavior of the stochastic model, also regarding of the basic reproduction number ℛ

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Global dynamics of a novel deterministic and stochastic SIR epidemic model with vertical transmission and media coverage

Advances in Difference Equations ◽

10.1186/s13662-020-03145-3 ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Xiaodong Wang ◽

Chunxia Wang ◽

Kai Wang

Keyword(s):

Vertical Transmission ◽

Epidemic Model ◽

Media Coverage ◽

Existence And Uniqueness ◽

Deterministic Model ◽

Reproduction Number ◽

Global Dynamics ◽

Sir Epidemic Model ◽

Sir Epidemic ◽

Stochastic Sir

AbstractIn this paper, we study a novel deterministic and stochastic SIR epidemic model with vertical transmission and media coverage. For the deterministic model, we give the basic reproduction number $R_{0}$ R 0 which determines the extinction or prevalence of the disease. In addition, for the stochastic model, we prove existence and uniqueness of the positive solution, and extinction and persistence in mean. Furthermore, we give numerical simulations to verify our results.

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A fractional order mathematical model for COVID-19 dynamics with quarantine, isolation, and environmental viral load

Advances in Difference Equations ◽

10.1186/s13662-021-03265-4 ◽

2021 ◽

Vol 2021 (1) ◽

Cited By ~ 2

Author(s):

Mohammed A. Aba Oud ◽

Aatif Ali ◽

Hussam Alrabaiah ◽

Saif Ullah ◽

Muhammad Altaf Khan ◽

...

Keyword(s):

Epidemic Model ◽

Reproduction Number ◽

Model Parameters ◽

Disease Dynamics ◽

Threshold Parameter ◽

Fractional Model ◽

Infected People ◽

Fractional Models ◽

Disease Epidemics ◽

The Impact

AbstractCOVID-19 or coronavirus is a newly emerged infectious disease that started in Wuhan, China, in December 2019 and spread worldwide very quickly. Although the recovery rate is greater than the death rate, the COVID-19 infection is becoming very harmful for the human community and causing financial loses to their economy. No proper vaccine for this infection has been introduced in the market in order to treat the infected people. Various approaches have been implemented recently to study the dynamics of this novel infection. Mathematical models are one of the effective tools in this regard to understand the transmission patterns of COVID-19. In the present paper, we formulate a fractional epidemic model in the Caputo sense with the consideration of quarantine, isolation, and environmental impacts to examine the dynamics of the COVID-19 outbreak. The fractional models are quite useful for understanding better the disease epidemics as well as capture the memory and nonlocality effects. First, we construct the model in ordinary differential equations and further consider the Caputo operator to formulate its fractional derivative. We present some of the necessary mathematical analysis for the fractional model. Furthermore, the model is fitted to the reported cases in Pakistan, one of the epicenters of COVID-19 in Asia. The estimated value of the important threshold parameter of the model, known as the basic reproduction number, is evaluated theoretically and numerically. Based on the real fitted parameters, we obtained $\mathcal{R}_{0} \approx 1.50$ R 0 ≈ 1.50 . Finally, an efficient numerical scheme of Adams–Moulton type is used in order to simulate the fractional model. The impact of some of the key model parameters on the disease dynamics and its elimination are shown graphically for various values of noninteger order of the Caputo derivative. We conclude that the use of fractional epidemic model provides a better understanding and biologically more insights about the disease dynamics.

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Spatial dynamics of a diffusive SIRI model with distinct dispersal rates and heterogeneous environment

Communications on Pure & Applied Analysis ◽

10.3934/cpaa.2021120 ◽

2021 ◽

Vol 0 (0) ◽

pp. 0

Author(s):

Lian Duan ◽

Lihong Huang ◽

Chuangxia Huang

Keyword(s):

Steady State ◽

Basic Reproduction Number ◽

Epidemic Model ◽

Reproduction Number ◽

Spatial Dynamics ◽

Heterogeneous Environment ◽

Threshold Parameter ◽

Dispersal Rate ◽

Siri Model ◽

The Basic Reproduction Number

<p style='text-indent:20px;'>In this paper, we are concerned with the dynamics of a diffusive SIRI epidemic model with heterogeneous parameters and distinct dispersal rates for the susceptible and infected individuals. We first establish the basic properties of solutions to the model, and then identify the basic reproduction number <inline-formula><tex-math id="M1">\begin{document}$ \mathscr{R}_{0} $\end{document}</tex-math></inline-formula> which serves as a threshold parameter that predicts whether epidemics will persist or become globally extinct. Moreover, we study the asymptotic profiles of the positive steady state as the dispersal rate of the susceptible or infected individuals approaches zero. Our analytical results reveal that the epidemics can be extinct by limiting the movement of the susceptible individuals, and the infected individuals concentrate on certain points in some circumstances when limiting their mobility.</p>

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PENGEMBANGAN MODEL EPIDEMIK SIRA UNTUK PENYEBARAN VIRUS PADA JARINGAN KOMPUTER

Journal of Fundamental Mathematics and Applications (JFMA) ◽

10.14710/jfma.v2i1.26 ◽

2019 ◽

Vol 2 (1) ◽

pp. 13

Author(s):

Panca Putra Pemungkas ◽

Sutrisno Sutrisno ◽

Sunarsih Sunarsih

Keyword(s):

Equilibrium Point ◽

Basic Reproduction Number ◽

Epidemic Model ◽

Computer Network ◽

Reproduction Number ◽

Equilibrium Points ◽

Virus Spread ◽

Computer Based ◽

Stability Issues ◽

Spread Analysis

This paper is addressed to discuss the development of epidemic model of SIRA (Susceptible-Infected-Removed-Antidotal) for virus spread analysis purposes on a computer network. We have developed the existing model by adding a possibility of antidotal computer returned to susceptible computer. Based on the results, there are two virus-free equilibrium points and one endemic equilibrium point. These equilibrium points were analyzed for stability issues using basic reproduction number and Routh-Hurwitz Method.

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