Mathematical Modelling of the HIV Pandemic
Understanding epidemic dynamics is essential for developing effective control strategies. Successful implementation of such strategies requires optimal operational decisions. Mathematical modelling is a powerful approach to aid in achieving these goals.
Containing the HIV pandemic has been extremely challenging, due to complexities on multiple levels, which span molecules to social groups. High mutation rate of the HIV virus, long infectious latent period with few clinical symptoms, potential for developing resistance to antiretroviral medication, complications arising from co-infections with other pathogens, biological variation in the population affecting susceptibility to HIV and socioeconomic factors that increase the vulnerability of some groups to HIV infection are examples of complicating factors.
Unlike any other disease, HIV/AIDS has brought attention to critical social problems, such as poverty, racism, discrimination, addictions and homelessness that are found repeatedly to be key drivers of the spread of infection. Over the last two decades, vast knowledge has been generated about the basic biology, natural history and social context of HIV. A more recent trend has been the application of mathematical modelling to understanding epidemic dynamics and developing ways to control the epidemic. This area of research is relatively new and holds much potential for growth.
The IMPACT-HIV group combines quantitative expertise in fields such as mathematics, theoretical physics and computer sciences with the principles of public health and epidemiology in collaborative projects to address critical issues encountered in efforts to contain the HIV/AIDS pandemic.
Current Projects
1. Mathematical modelling of the spread and control of HIV among injection drug users
It is now increasingly accepted that expanded access to antiretroviral treatment will play a central role in efforts to contain and reverse the HIV pandemic. Therefore, it is essential to understand how Treatment as Prevention programs can be implemented most effectively on a large scale and how they are best combined with other biomedical and behavioural interventions for maximum benefit.
In this group of projects we use various mathematical modelling techniques to develop and evaluate the potential population health benefit of combination strategies for HIV prevention. Using a software package (NepidemiX) developed by the IMPACT-HIV group, we develop network models for specific risk-groups or settings to provide us with solutions that take into account local conditions, which are often critical in Examples of projects within this theme include:
- Estimating the herd immunity for combination prevention strategies in an urban injection drug user community
- Assessing the role of risk behaviour in the population-level prevention of HIV transmission through large-scale expansion of access to antiretroviral therapy
2. Estimation of Epidemiological Parameters for Evaluating Interventions
The best measure of the state of the HIV epidemic and the effectiveness of interventions in reducing HIV transmission is a change in the number of new HIV infections, or HIV incidence. However, due to the delayed presentation of HIV symptoms, it has proven very difficult to measure or estimate HIV incidence. The number of new diagnoses is a commonly used proxy for incidence but this is a poor approximation to the actual number of new infections. Currently available biological assays to measure incidence are still not broadly applicable and reliable. Cohort studies are also conducted to measure incidence but these are expensive and complicated and their results are specific to the population studied.
The goal of this group of projects is to address the need for reliable estimates of HIV incidence and related epidemiological parameters. To accomplish this, we are developing mathematical approaches to estimating epidemiological parameters from readily available surveillance data to derive near real-time feedback on the course of the HIV epidemic and the impact of interventions. The following projects address these issues:
- Estimating HIV incidence in British Columbia, Canada, using readily available surveillance data
- Estimating the proportion of undiagnosed infections and the annual HIV transmission rate using surveillance data
- Estimating coverage of Highly Active Antiretroviral Therapy in the City of New York
3. Improving, Monitoring and Evaluating Delivery of HIV Health Services
Implementation of interventions raises many operational questions and challenges. For example, it is often important to know how a promising prevention strategy would impact the health care system as a whole, or what is the optimal allocation of resources in order to achieve the desired population health outcome. The field of operational research deals with such issues.
IMPACT-HIV is constructing models that evaluate how operational decisions and dynamical changes in the HIV epidemic impact one another. We currently have two projects in this area:
- Evaluating the impact of expanded access to antiretroviral therapy on the cost and utilisation of health care services in Vancouver, British Columbia
- Developing surveillance-based indicators for the success of Treatment as Prevention programs implemented through “Seek, Test, Treat and Retain” strategies
4. Nepidemix – A Network Modelling Software to Study Epidemics
Network modelling is particularly useful in understanding how heterogeneity in individual characteristics and behaviors contribute to HIV transmission risk. Results in mathematical epidemiology that emerged over the past decade suggests that the structure of a person’s behavioral network may have a strong influence on their risk of acquiring HIV or other infections. Network structure also seems to be an important determinant of how effectively prevention strategies contain the spread of HIV in the population.
Network simulations can provide critical insights into such issues but network models are difficult to construct. To facilitate the application of network modelling to a wide range of questions, the IMPACT-HIV group has developed the NepidemiX software package.
NepidemiX features a highly configurable simulation class, and processes that may be configured using an easy to read script or implemented in the powerful Python programming language. In other words, the highly configurable NepidemiX design allows easy construction of models for specific situations and questions. NepidemiX is uniquely equipped for investigations into the influence of network structure on epidemic dynamics. Instead of generating a single network structure and keeping it fixed, NepidemiX allows network parameters to be varied within a single model.
The IMPACT-HIV group mainly uses NepidemiX for studies of HIV-related issues, the software is suitable for epidemiological simulations in a broader context, and can be adopted to study general network processes.
Collaborations
IMPACT-HIV is a collaboration of the British Columbia Centre for Excellence in HIV/AIDS and the Complex Systems Modeling Group at the IRMACS Centre at Simon Fraser University.
We also collaborate with the following institutions:
- Vancouver Coastal Health
- British Columbia Centre for Disease Control
- Faculty of Health Sciences, Simon Fraser University
- Department of Mathematics, Simon Fraser University
