Can Difficult-to-Reuse Syringes Reduce the Spread of HIV Among Injection Drug Users? -Caulkins, Kaplan, Lurie, O’Connor & Ahn Presented by: Arifa Sultana Zoila Guerra Vikram Sriram

Outline  Introduction  Models  Model I - One type of syringe  Model II - Multiple type of syringe  Future work

Introduction  Principal cause of HIV  Prevention/controlling methods  Using syringes that is impossible to reuse. (may not be feasible)  Distributing Difficult-to-reuse (DTR) syringes

Design approaches for DTR 1. Syringes containing hydrophilic gel 2. Plungers disabled when reload 3. Needles disabled after the first use 4. Valves that prevent second loading

Benefits of DTR  Reduce the frequency of reused syringes  Reduce the syringes sharing with other

Objectives of the paper  Proportion of injections that are potentially infectious and transmit HIV (i.e. proportion infectious injection)  Which effect would be greater?  Regular  DTR+ Regular

Assumptions  Total number of syringes and the frequency of injection remain constant.  Consider only intentional injections.  Here the syringe is treated as infinitely lived.

Model I – One type of Syringe  To find out the impact of DTR in spread of HIV  How often an injection drug users (IDU’s) injects with an infectious syringe.  Kaplan [1989] introduced one type syringe model considering syringe’s perspective.

How this model differ from Kaplan’s [1989] model?  Kaplan[1989]: changes in the proportion of number of IDU's who are infected and changes in proportion of number of syringes which are infected. This paper: on the proportion of injections that are made with infectious syringes.  Kaplan[1989]: one type of syringe This paper: one and multiple types of syringes  Kaplan [1989]: followed individual syringes This paper: Sequence of syringes in succession  Kaplan [1989]: Used differential equations This paper: Discrete-time Markov model

Model I (Cont.)  Discrete-time Markov model: Find the probability that the syringe is infectious  The epochs are the instants of time just before a session in which a syringe is used to inject drugs.  At each epoch a syringe can be in two states :  Uninfectious (U)  Infectious (I)  Probability from uninfectious to infectious P UI  Probability from infectious to uninfectious P IU

Model I (Cont.) How a Un-infectious Infectious?  Used by infected user = the probability of use by an infected user  Become infectious through that use = the probability become infectious through that use  Remain infectious until just before subsequent use = probability of remain infectious until just before subsequent use. = probability that a syringe which is infectious immediately after use, ceases to be infectious before its next use.

Model I (Cont.) Probability of uninfectious syringe become infectious P UI = f φ (1- ω)

Model I (Cont.) How a infectious un infectious 1. Both used by an uninfected user = probability of both used by an uninfected user. Have that use render the syringe un-infectious = probability that the use renders the syringe un-infectious 2. Cease to be infectious between uses (by killing virus or replacing syringe) = probability of cease to be infectious between uses

Model I (Cont.) Probability of infectious syringe become uninfectious p UI =(1- f)θ+(1-(1-f)θ)ω) here ω = Where = probability of “dry out”/killing virus n = mean of geometric random variable

Model II  There is more than one type of syringe  The overall fraction of potentially infectious is the weighted sum of the fractions for each type of syringe.  Focus on two types of syringes.  How the proportion of infectious injections would change if DTR syringes are introduced into the current environment

Model II (Cont.) The outcome depends on: Number of both DTR and regular syringes consumed after the DTR syringes are introduced compares to the number of regular syringes consumed before DTR syringes are introduced.

Model II (Cont.) s = rate of consumption of syringes introduced by intervention/rate of consumption of regular syringes before the intervention r = change in rate of consumption of regular syringes caused by intervention/rate of consumption of regular syringes before intervention

Model II (Cont.) If the number of injections remains the same after the introduction of DTR syringes, n R =(1+r)n’ R +sn D where = average number of times a DTR syringe is used = average number of times a regular syringe was used before DTR syringes were introduced = average number of times regular syringes are used after DTR are introduced

Future work  Finding proportion of infectious injections for both models  Explaining properties of the model  Estimating parameter values  Numerical estimates

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