Inferring model parameters in network-based disease simulation

Abstract

Many models of infectious disease ignore the underlying contact structure through which the disease spreads. However, in order to evaluate the efficacy of certain disease control interventions, it may be important to include this network structure. We present a network modeling framework of the spread of disease and a methodology for inferring important model parameters, such as those governing network structure and network dynamics, from readily available data sources. This is a general and flexible framework with wide applicability to modeling the spread of disease through sexual or close contact networks. To illustrate, we apply this modeling framework to evaluate HIV control programs in sub-Saharan Africa, including programs aimed at concurrent partnership reduction, reductions in risky sexual behavior, and scale up of HIV treatment.

Appendix: Details of Tanzania example

This Appendix describes input parameters and key assumptions for the example analysis of the effects of concurrency reduction and other HIV prevention programs in Tanzania. Values for all input parameters are shown in Table 1.

Table 1 Input parameters for numerical example evaluating the effects of concurrency reduction and other HIV prevention programs in Tanzania

We initialized the model with approximately 8,000 sexually active and potentially sexually active individuals aged 15–49 years old. We matched the age distribution of this population to gender-specific age distributions of Tanzania. Individuals age into the population at age 15 with an annual maturation rate determined from Tanzania demographic data [35]. Individuals experience a baseline gender- and age-specific mortality risk determined from country-specific life tables [42]. We matched the gender-specific concurrent partnership behavior reported in the most recent Demographic Health Survey conducted in Tanzania [24].

The disease model is a simplified version of a previously developed HIV progression model [5] and is described in detail in [8].

We modeled three discrete HIV disease states: acute, chronic, and on treatment. The HIV disease state determined the risk of transmission to sexual partners, with the acute state having the highest transmission risk and the treated state having the lowest. Per-act transmission probabilities were obtained from the literature [39] and then adjusted in model calibration to account for levels of sexual activity and condom use so that model-projected prevalence matched projected HIV prevalence trends in Tanzania.

We also modeled each individual’s CD4 counts. This provides a continuous measure of an individual’s immune function. CD4 counts determined HIV-related mortality risk and risks of opportunistic infections, which also increased mortality. In the chronic HIV state, CD4 counts decline slowly over time. Once CD4 counts fall below 200 cells/μL, an individual becomes HIV treatment eligible. HIV treatment causes a recovery in CD4 counts and thus a reduction in HIV-related mortality, though not all eligible individuals receive treatment in these resource-limited settings. The level of treatment coverage in Tanzania is estimated to be about 30% [34].