![](/images/graphics-bg.png)
A Stochastic Differential Equation Model for the Spread of HIV amongst People Who Inject Drugs
Joint Authors
Mao, Xuerong
Liang, Yanfeng
Greenhalgh, David
Source
Computational and Mathematical Methods in Medicine
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-03-09
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
We introduce stochasticity into the deterministic differential equation model for the spread of HIV amongst people who inject drugs (PWIDs) studied by Greenhalgh and Hay (1997).
This was based on the original model constructed by Kaplan (1989) which analyses the behaviour of HIV/AIDS amongst a population of PWIDs.
We derive a stochastic differential equation (SDE) for the fraction of PWIDs who are infected with HIV at time.
The stochasticity is introduced using the well-known standard technique of parameter perturbation.
We first prove that the resulting SDE for the fraction of infected PWIDs has a unique solution in (0, 1) provided that some infected PWIDs are initially present and next construct the conditions required for extinction and persistence.
Furthermore, we show that there exists a stationary distribution for the persistence case.
Simulations using realistic parameter values are then constructed to illustrate and support our theoretical results.
Our results provide new insight into the spread of HIV amongst PWIDs.
The results show that the introduction of stochastic noise into a model for the spread of HIV amongst PWIDs can cause the disease to die out in scenarios where deterministic models predict disease persistence.
American Psychological Association (APA)
Liang, Yanfeng& Greenhalgh, David& Mao, Xuerong. 2016. A Stochastic Differential Equation Model for the Spread of HIV amongst People Who Inject Drugs. Computational and Mathematical Methods in Medicine،Vol. 2016, no. 2016, pp.1-14.
https://search.emarefa.net/detail/BIM-1100173
Modern Language Association (MLA)
Liang, Yanfeng…[et al.]. A Stochastic Differential Equation Model for the Spread of HIV amongst People Who Inject Drugs. Computational and Mathematical Methods in Medicine No. 2016 (2016), pp.1-14.
https://search.emarefa.net/detail/BIM-1100173
American Medical Association (AMA)
Liang, Yanfeng& Greenhalgh, David& Mao, Xuerong. A Stochastic Differential Equation Model for the Spread of HIV amongst People Who Inject Drugs. Computational and Mathematical Methods in Medicine. 2016. Vol. 2016, no. 2016, pp.1-14.
https://search.emarefa.net/detail/BIM-1100173
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1100173