Intravenous drug use and tattooing remain one of the major routes of HIV/AIDS transmission among prisoners. We formulate and analyze a deterministic model for the role of intravenous drug use in HIV/AIDS transmission among women prisoners. With the aid of the Centre Manifold theory, the endemic equilibrium is shown to be locally asymptotically stable when the corresponding reproduction number is greater than unity. Analysis of the reproduction number and numerical simulations suggest that an increase in intravenous drug use among women prisoners as they fail to cope with prison settings fuels the HIV/AIDS epidemic in women prisoners. Failure to control HIV/AIDS among female prisoners may be a time bomb to their communities upon their release. Thus, it may be best to consider free needle/syringe exchange and drug substitution treatment programmes in women prisons as well as considering open prison systems for less serious crimes.
The imprisonment of large numbers of drug addicts has the potential to create environments within which social networks that enhance the transmission of infectious diseases form [
In many jurisdictions, a larger proportion of women than men are in prison for drug related offences [
Women constitute a very small proportion of the total prison population, globally accounting 5% of the total prison population [
The rest of this paper is organized as follows. In the next section, the model and its basic properties are presented. In Section
Consider a population consisting of the following subpopulations: susceptible female prisoners nondrug injectors
Model flow diagram.
From the assumptions on the dynamics of the epidemic made above, the following are the model equations:
Model system (
The disease-free equilibrium
In terms of the HIV and drug induction forces of infection
It can be shown from
The endemic equilibrium point
In this section, we carry out detailed numerical simulations using Matlab programming language to assess the transmission dynamics of HIV in prisons housing female prisoners. The parameter values that we use for numerical simulations are in Table
Model parameters and their interpretations.
Parameter | Symbol | Value | Source |
---|---|---|---|
Recruitment rate |
|
0.00163 yr−1 |
NPA |
Natural mortality rate |
|
0.02 yr−1 |
|
Natural rate of progression to AIDS |
|
0.1 yr−1 |
|
Modification parameter |
|
0.25 | Assumed |
AIDS related death rate |
|
0.4 yr−1 |
|
Product of effective contact rate for HIV infection and probability of HIV transmission per drug injection |
|
0.562 yr−1 |
|
Rate of becoming a drug user |
|
0.4 yr−1 |
|
Rate of quitting drug misuse of sickness |
|
0.3 yr−1 |
|
Rate of release from prison |
|
0.25 yr−1 | Assumed |
Proportion recruited into |
|
0.375, 0.125, 0.375, 0.125 | Assumed |
In Table
Figure
Simulations of model system (
Figure
Time series evolution of the HIV-only infected individuals and those displaying symptoms of AIDS for various initial conditions when all female prisoners are made of nondrug users and when they are all intravenous users. Parameter values used are in Table
A mathematical model has been presented in attempt to understand the transmission dynamics of HIV/AIDS among female prisoners with particular reference to female prisoners in Zimbabwe. Drug use in female prisons is two way: (i) sharing of unsterile needles/syringes enhances the transmission of HIV and (ii) flashing blood that is drawing blood from someone who has injected herself with a drug and inject the blood into herself on its own exposes the injector to the HIV infection. Analysis of the reproduction number has shown that (i) a reduction in drug use results in a decrease of HIV/AIDS prevalence among female prisoners and (ii) release of prisoners may also act in reducing the concentration HIV/AIDS cases in prisons. The latter fact is not feasible, but perhaps implementing opening prison systems where prisoners of less serious crimes are allowed to serve their sentences while staying with their families enables female prisoners to cope with stressful prison conditions. Open prison systems will reduce the influence of peer pressure among prisoners as they will have moral and psychological support from the family which does not exist in enclosed female prison systems. Numerical simulations carried out also support the analytic results that increase in drug use and tattooing increases HIV/AIDS prevalence among women prisoners. The result of this study has a public health implication considering high rates of syringe lending and borrowing in prisons. This might explain why there are more HIV cases in prisons than the general population in the case of the USA [