Our Work

Mathematical Modelling of the HIV Epidemic

The HIV pandemic has been extremely difficult to contain due to complex challenges on multiple levels, spanning molecules to social groups. The high mutation rate of HIV, the long infectious latent period with few clinical symptoms, the 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 some factors that create challenges in controlling the epidemic.

More than perhaps any other disease, HIV/AIDS has brought attention to persistent problems in our communities – including stigma and discrimination, addictions and poverty – that are also key drivers of the spread of infection. Mathematical models are powerful tools for exploring epidemic dynamics and for informing the development of intervention strategies. The IMPACT-HIV group applies mathematical modelling in collaborative projects engaging government and public health partner organisations to inform planning, programming and policy for improved interventions to address the HIV epidemic locally and internationally.

Current Projects

Using Antiretroviral Treatment as HIV Prevention

Expanding access to highly active antiretroviral therapy (HAART) has become the cornerstone of comprehensive HIV prevention strategies globally. HAART dramatically improves symptoms of HIV infections and reduces HIV transmission. We seek to understand effective measures for large-scale expansion of HAART coverage to simultaneously improve treatment and prevention outcomes. We also study optimal ways to combine treatment expansion with other biomedical and behavioural interventions for individual and community benefits.

Currently, our main projects employ ordinary differential equation (ODE) models and network models of HIV epidemics affecting injection drug using communities in British Columbia, and female sex workers, men who have sex with men and transgender communities in the Republic of Panama. Our models incorporate dynamic representations of risk behaviour as social contagion to allow a thorough evaluation of the role risk behaviour in preventing HIV transmission through expansion of treatment coverage.

Operations Research to Improve HIV Health Service Delivery

Implementing HIV interventions raises many practical operational questions and challenges. For example, it is often important to know how a potential prevention strategy could impact the utilization of health services, or what resource allocation strategy is optimal for achieving specific service delivery and population health outcomes. The field of operational research deals with such issues.

In this project we use system dynamics, agent-based simulation, network modelling and analytical techniques to optimize health service operations to improve the delivery of HIV care and treatment in Vancouver, British Columbia. We developed a model of the continuum of HIV care in Vancouver, which incorporates activities and decision points involving health care services for HIV testing, linkage to care, treatment and long-term retention in care and treatment. We use this model to optimize the distribution of resources among health care services within Vancouver’s HIV testing and treatment programs to improve planning and programming. We also perform system optimization by considering resource allocation scenarios across the entire continuum of HIV care to achieve optimal service delivery and population health outcomes.

Estimating HIV Incidence

The best measure for the state of the HIV epidemic and effectiveness of interventions is a change in the number of new HIV infections over time - or HIV incidence. Due to delayed presentation of symptoms, it has proven difficult to measure or estimate HIV incidence. A common proxy is the number of diagnoses but this is a poor approximation to the actual number of new infections.

In this project, we combine readily available surveillance data and viral genetic data to develop separate models for HIV incidence and apply mathematical optimization methods to reconcile these, thereby generating incidence estimates. This approach provides an internal validation of each of the models.

NepidemiX – Open Source Network Modelling Software to Study Epidemics

Network models can be used to explore the role of heterogeneity in individual characteristics and behaviours in HIV transmission risk. Results in mathematical epidemiology over the past decade suggest that social network structure has a strong influence on the risk of acquiring HIV or other infections. Network structure is also an important determinant of the effectiveness of prevention strategies to contain the spread of HIV in the population.

Network simulations can provide critical insights into such issues; however, network models are difficult to construct. The NepidemiX software package, developed by Lukas Ahrenberg and IMPACT-HIV, facilitates the rapid construction of network models for a wide variety of applications.

NepidemiX features a highly configurable simulation class, and processes that may be specified using an easy-to-read script, or implemented in the powerful Python programming language. Although NepidemiX can be used for any application involving networks, it is uniquely equipped for investigating 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.

Nepidemix can be downloaded here.


IMPACT-HIV is a collaboration of the British Columbia Centre for Excellence in HIV/AIDS and the Complex Systems Modelling Group at the IRMACS Centre at Simon Fraser University.

We also collaborate with the following organisations:

Vancouver Coastal Health
British Columbia Centre for Disease Control
Faculty of Health Sciences, Simon Fraser University
Department of Mathematics, Simon Fraser University
Government of Panama