Projects per year
Abstract
In this paper, 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 [10]. This was based on the original model constructed by Kaplan [17] 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 t. The stochasticity is introduced using the wellknown 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 also 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. Hence in situations where stochastic noise is important predictions of control measures such as needle cleaning or reduction of needle sharing rates needed to eliminate disease may be overly conservative.
Original language  English 

Article number  6757928 
Number of pages  14 
Journal  Computational and Mathematical Methods in Medicine 
Volume  2016 
DOIs  
Publication status  Published  10 Mar 2016 
Keywords
 HIV
 AIDS
 parameter perturbation
 extinction
 persistence
 stationary distribution
 stochastic differential equations
 Brownian motion
 environmental stochasticity
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Projects
 3 Finished

Numerical Analysis of Stochastic Differential Equations: New Challenges
1/10/15 → 30/09/17
Project: Research Fellowship

Epsrc Doctoral Training Grant  Liang, Yanfeng
Greenhalgh, D., Mao, X. & Liang, Y.
EPSRC (Engineering and Physical Sciences Research Council)
1/10/12 → 3/10/16
Project: Research Studentship  Internally Allocated

Epsrc Doctoral Training Grant / RA8099
EPSRC (Engineering and Physical Sciences Research Council)
1/10/12 → 30/09/16
Project: Research Studentship  Internally Allocated
Datasets

A Stochastic Differential Equation Model for the Spread of HIV Amongst People Who Inject Drugs
Liang, Y. (Creator), Greenhalgh, D. (Creator) & Mao, X. (Creator), University of Strathclyde, 2015
DOI: 10.15129/bf5ba8b5d48443c7800614fb76819be2
Dataset