Nonrandom Mixing Models of HIV Transmission. In: Castillo-chavez C, editor. Mathematical and Statistical Approaches to AIDS Epidemiology. Berlin: Springer Berlin Heidelberg; 1989. pp. 218-39. [DOI: 10.1007/978-3-642-93454-4_10]

Risk stratification in compartmental epidemic models: Where to draw the line?

Economic evaluations of infectious disease control interventions frequently use dynamic compartmental epidemic models. Such models capture heterogeneity in risk of infection by stratifying the population into discrete risk groups, thus approximating what is typically continuous variation in risk. An important open question is whether and how different risk stratification choices influence model predictions of intervention effects. We develop equivalent Susceptible-Infected-Susceptible (SIS) dynamic transmission models: an unstratified model, a model stratified into a high-risk and low-risk group, and a model with an arbitrary number of risk groups. Absent intervention, the models produce the same overall prevalence of infected individuals in steady state. We consider an intervention that either reduces the contact rate or increases the disease clearance rate. We develop analytical and numerical results characterizing the models and the effects of the intervention. We find that there exist multiple feasible choices of risk stratification, contact distribution, and within- and between-group contact rates for models that stratify risk. We show analytically and empirically that these choices can generate different estimates of intervention effectiveness, and that these differences can be significant enough to alter conclusions from cost-effectiveness analyses and change policy recommendations. We conclude that the choice of how to discretize risk in compartmental epidemic models can influence predicted effectiveness of interventions. Therefore, analysts should examine multiple alternatives and report the range of results.

Mathematical models of contact patterns between age groups for predicting the spread of infectious diseases

The spread of an infectious disease is sensitive to the contact patterns in the population and to precautions people take to reduce the transmission of the disease. We investigate the impact that different mixing assumptions have on the spread an infectious disease in an age-structured ordinary differential equation model. We consider the impact of heterogeneity in susceptibility and infectivity within the population on the disease transmission. We apply the analysis to the spread of a smallpox-like disease, derive the formula for the reproduction number, ~0, and based on this threshold parameter, show the level of human behavioral change required to control the epidemic. We analyze how different mixing patterns can affect the disease prevalence, the cumulative number of new infections, and the final epidemic size. Our analysis indicates that the combination of residual immunity and behavioral changes during a smallpox-like disease outbreak can play a key role in halting infectious disease spread; and that realistic mixing patterns must be included in the epidemic model for the predictions to accurately reflect reality.

The cost-effectiveness of counseling strategies to improve adherence to highly active antiretroviral therapy among men who have sex with men

OBJECTIVE

Inadequate adherence to highly active antiretroviral therapy (HAART) may lead to poor health outcomes and the development of HIV strains that are resistant to HAART. The authors developed a model to evaluate the cost-effectiveness of counseling interventions to improve adherence to HAART among men who have sex with men (MSM).

METHODS

The authors developed a dynamic compartmental model that incorporates HIV treatment, adherence to treatment, and infection transmission and progression. All data estimates were obtained from secondary sources. The authors evaluated a counseling intervention given prior to initiation of HAART and before all changes in drug regimens, combined with phone-in support while on HAART. They considered a moderate-prevalence and a high-prevalence population of MSM.

RESULTS

If the impact of HIV transmission is ignored, the counseling intervention has a cost-effectiveness ratio of $25,500 per quality-adjusted life year (QALY) gained. When HIV transmission is included, the cost-effectiveness ratio is much lower: $7400 and $8700 per QALY gained in the moderate- and high-prevalence populations, respectively. When the intervention is twice as costly per counseling session and half as effective as estimated in the base case (in terms of the number of individuals who become highly adherent, and who remain highly adherent), then the intervention costs $17,100 and $19,600 per QALY gained in the 2 populations, respectively.

CONCLUSIONS

Counseling to improve adherence to HAART increased length of life, modestly reduced HIV transmission, and cost substantially less than $50,000 per QALY gained over a wide range of assumptions but did not reduce the proportion of drug-resistant strains. Such counseling provides only modest benefit as a tool for HIV prevention but can provide significant benefit for individual patients at an affordable cost.

Rational behavioral response and the transmission of STDs

The susceptible-infected (SI) model is extended by allowing for individual optimal choices of self-protective actions against infection, where agents differ with respect to preferences and costs of self-protection. It is shown that a unique endemic equilibrium prevalence exists when the basic reproductive number of a STD is strictly greater than unity, and that the disease-free equilibrium is the unique steady state equilibrium when the basic reproductive number is less than or equal to one. Unlike in models that take individual behavior as given and fixed, the endemic equilibrium prevalence need not vary monotonically with respect to the basic reproductive number. Specifically, with endogenously determined self-protective behavior, a reduction in the basic reproductive number may in fact increase the endemic equilibrium prevalence. The global stability of the endemic steady state is established for the case of a homogeneous population by showing that, for any non-zero initial disease prevalence, there exists an equilibrium path which converges to the endemic steady state.

Cost-effectiveness of harm reduction in preventing hepatitis C among injection drug users

OBJECTIVES

Hepatitis C (HCV) has emerged as a major epidemic among injection drug users (IDUs), with observed prevalence exceeding 70% in many American and European cities. This article explores the potential of syringe exchange programs (SEPs) to reduce HCV incidence and prevalence.

DESIGN

A random-mixing epidemiological model is used to examine the potential impact of harm reduction interventions.

METHODS

Steady-state analysis is used to scrutinize the impact of SEP on HCV incidence and prevalence and to examine the accuracy of short-term incidence analysis in predicting long-run program effects.

RESULTS

SEP is predicted to have little impact on HCV incidence and prevalence within realistic populations of IDUs.

CONCLUSIONS

Short-term incidence analysis substantially overstates SEP effectiveness and cost-effectiveness in preventing HCV. More comprehensive harm reduction models, coupled with referral of active IDUs to treatment, must complement syringe exchange to successfully contain highly infectious blood-borne diseases.

Implicit valuation of a blood-exclusion decision

This paper presents an implicit valuation of Israel's decision to exclude blood donations from Ethiopian immigrants. The approach adopts assumptions that deliberately overstate the public health effectiveness of this policy, for if such an analysis fails to justify exclusion on public health grounds, nothing will. Building on a recent (over)estimate of the number of infectious donations prevented by the ban, the analysis considers the cost of HIV-infectious donations entering the blood supply, the benefits of healthy donations, and the cost of needlessly screening blood that will be discarded without regard to the test result. The analysis also highlights the social costs of excluding donors on the basis of ethnicity. The possibility of downstream HIV transmission from transfusion recipients infected from contaminated blood is also considered. All such calculations are made in a manner that deliberately favors the exclusion decision. In spite of such a one-sided analysis, the author concludes that the exclusion policy is not justifiable on cost-benefit grounds if the social costs of exclusion exceed $218,000 per year, or $3.63 per Ethiopian immigrant annually.

The effect of changing sexual activity on HIV prevalence

In a one-sex preferred mixing model, reductions in the rate of partner change by those with low sexual activity increase the average probability of HIV infection in the remaining pool of available partners. This increases prevalence among people with high activity, and since high activity people disproportionately influence the spread of HIV, may increase long-run prevalence in the population as a whole. Calculations using the model and survey data on sexual activity indicate that in low prevalence populations, many people have low enough activity that reductions in their activity might increase the endemic steady-state prevalance. If these results prove robust in more realistic models, they would support the case for targeting public health messages urging reduced sexual activity to high activity people.

Asymptotic worst-case mixing in simple demographic models of HIV/AIDS

The majority of published modeling work regarding the impact of mixing patterns among subgroups on the spread of HIV infection assumes either that the overall population size remains constant, the aggregate immigration to the population occurs at a constant annual rate, or that no immigration occurs and the population in question declines due to HIV or other causes. In this paper, immigration rates are modeled as simple functions of population size and may be interpreted as aggregate birth rates. This assumption implies asymptotic exponential growth in the disease-free population as long as per capita birth rates exceed per capita mortality rates. The introduction of HIV infection to such a population may change this situation, and the asymptotic population growth rate can be reduced substantially as a result. The specific manner in which this occurs depends in part upon difficult to observe mixing patterns among those with different sexual activity rates. Rather than attempting to explicitly model a variety of mixing patterns, a bound on the impact of worst-case mixing is produced, where "worst case" refers to the mixing pattern that maximizes the asymptotic prevalence of infection, which is equivalent to minimizing the asymptotic population growth rate. These new techniques are illustrated with a numerical example.

Heterogeneous sexual mixing in populations with arbitrarily connected multiple groups

"A simple procedure for constructing [social/sexual] mixing models for arbitrarily classified (e.g. by sex, age, geographical location, sexual preference) populations is outlined, including a scheme for finding the number of independent mixing parameters required, and a simple (linear algebra) means for finding the values of the dependent mixing parameters. Various worked examples are presented, including the two-sex problem and structured and selective mixing." The use of the models for analyzing mixing structures for AIDS transmission is assessed. (SUMMARY IN FRE)