Alexander R. Rutherford

Changing Risk Behaviours and the HIV Epidemic: A Mathematical Analysis in the Context of Treatment as Prevention

Background Expanding access to highly active antiretroviral therapy (HAART) has become an important approach to HIV prevention in recent years. Previous studies suggest that concomitant changes in risk behaviours may either help or hinder programs that use a Treatment as Prevention strategy. Analysis We consider HIV-related risk behaviour as a social contagion in a deterministic compartmental model, which treats risk behaviour and HIV infection as linked processes, where acquiring risk behaviour is a prerequisite for contracting HIV. The equilibrium behaviour of the model is analysed to determine epidemic outcomes under conditions of expanding HAART coverage along with risk behaviours that change with HAART coverage. We determined the potential impact of changes in risk behaviour on the outcomes of Treatment as Prevention strategies. Model results show that HIV incidence and prevalence decline only above threshold levels of HAART coverage, which depends strongly on risk behaviour parameter values. Expanding HAART coverage with simultaneous reduction in risk behaviour act synergistically to accelerate the drop in HIV incidence and prevalence. Above the thresholds, additional HAART coverage is always sufficient to reverse the impact of HAART optimism on incidence and prevalence. Applying the model to an HIV epidemic in Vancouver, Canada, showed no evidence of HAART optimism in that setting. Conclusions Our results suggest that Treatment as Prevention has significant potential for controlling the HIV epidemic once HAART coverage reaches a threshold. Furthermore, expanding HAART coverage combined with interventions targeting risk behaviours amplify the preventive impact, potentially driving the HIV epidemic to elimination.

Optimizing an HIV testing program using a system dynamics model of the continuum of care

Realizing the full individual and population-wide benefits of antiretroviral therapy for human immunodeficiency virus (HIV) infection requires an efficient mechanism of HIV-related health service delivery. We developed a system dynamics model of the continuum of HIV care in Vancouver, Canada, which reflects key activities and decisions in the delivery of antiretroviral therapy, including HIV testing, linkage to care, and long-term retention in care and treatment. To measure the influence of operational interventions on population health outcomes, we incorporated an HIV transmission component into the model. We determined optimal resource allocations among targeted and routine testing programs to minimize new HIV infections over five years in Vancouver. Simulation scenarios assumed various constraints informed by the local health policy. The project was conducted in close collaboration with the local health care providers, Vancouver Coastal Health Authority and Providence Health Care.

Control of an HIV epidemic among injection drug users: simulation modeling on complex networks

HIV remains a serious public health problem in many marginalized communities. We develop a network model of the HIV epidemic affecting injection drug users and female sex workers in the Downtown Eastside neighborhood of Vancouver, Canada, calibrated using data from public health surveillance and cohort studies. Many HIV positive individuals are unaware of their status and strategies for testing are an important part of HIV response programs. Upon diagnosis, HIV patients enter a continuum of care, involving both engagement and retention in treatment. We explored potential epidemic control strategies through simulation: reduced syringe sharing during injection drug use, reduced time to diagnosis, reduced time to initiation of treatment following diagnosis, and improved retention in treatment. We find that syringe sharing, HIV testing, and retention in treatment significantly impact HIV prevalence. Close connections between syringe sharing and sexual networks deserve attention as important avenues for rapid HIV transmission.

Matching models of HIV-1 viral dynamics to clinical data

Creating individualized within-host multiple phase disease models of HIV-1 infection has long been a goal of mathematicians and biologists. The challenge is in trying to build models that are representative of the disease, include realistic parameter estimates, and are able to incorporate a changing model structure. In this paper, we propose a fitting procedure, motivated by the biology of the disease, for matching parameters of differential equation and stochastic models of HIV-1 infection to data, which leverages high performance computing resources. The search uses knowledge of the biological set points to restrict the search domain, and parallel simulated annealing to match the model to acute and early chronic phase patient data. We highlight this method by finding parameters for two interconnected models of HIV-1 infection which we have developed. The high quality of our data allows us to model not only viral data, but also CD4 count data through the acute and chronic phases of the disease. The time span of our model exceeds that of previous models. The algorithm is able to find parameter values for four patients consistent with literature ranges and display individual set point equilibration and disease progression for both clinical markers.

High-Level Simulation Model of a Criminal Justice System

Criminal justice systems are complex. They are composed of several major subsystems, including the police, courts, and corrections, which are in turn composed of many minor subsystems. Predicting the response of a criminal justice system to changes in subsystems is often difficult. Mathematical modeling can serve as a powerful tool for understanding and predicting the behavior of these systems under different scenarios. In this chapter, we provide the process flow of the criminal justice system of the British Columbia, Canada. We further develop a system dynamics model of the criminal justice system, and show how this model can assist strategic decision-makers and managers make better decisions.

Mathematical Modelling to Evaluate Measures and Control the Spread of Illicit Drug Use

Millions of street-involved-youth worldwide are vulnerable to using and trading illicit drugs, which also place this group at high risk of drug-related criminality and health problems. It is often the case that drug users begin trafficking under the social influences within the drug culture to generate income for supporting their drug habits. The relative merits of behavioural (primary) or law enforcement (secondary) interventions for controlling the spread of drug use are widely debated. In this paper, we develop a network model to evaluate the effectiveness of modelling strategies. A network model with traffickers, current drug users and potential users is constructed. Traffickers exert social influence on current users to deal drugs and on potential users to initiate drug use. Primary intervention prevents potential users from initiating drug use while secondary intervention acts to reduce initiation into trafficking. To accomplish this, we vary the hypothetical social influence parameters in the model. Next, we analyze the properties of this system using dynamical system methods including mean field approximation (MFA), fixed point theory and bifurcation analysis. Furthermore, to evaluate the relative effectiveness of the two interventions, we study the properties of the phase transition between a drug-free and a drug-endemic state at equilibrium mathematically. Drug-free and drug-endemic states are separated by a curved phase transition. Via the shape of the phase transition curve we obtain the optimal intervention. Our findings confirm that a combination of primary and secondary interventions is the optimal intervention strategy. The optimal mixture of the two strategies depends on the relative numbers of drug users and traffickers.