# Infectious Diseases and Mathematical Modelling

• Why does HIV prevalence and incidence vary so widely within single countries?
• How do people (individuals and groups) spread diseases?
• To what extent do hospitalised influenza patients differ from patients diagnosed with influenza by primary care physicians? How can we be better prepared for the next influenza epidemic or pandemic?
• What is the optimal screening and treatment strategy for hepatitis C in Switzerland?
• How should a fixed amount of money best be allocated to reduce the number of new HIV infections and HIV-related deaths?
• What are the main drivers of loss-to-care in HIV-infected pregnant women in Malawi?
• Can probabilistic record linkage help track patients across health facilities?
• Is diabetes incidence increasing in HIV-infected patients in Zimbabwe?

These are examples of questions the division Infectious diseases and mathematical modelling is trying to answer. The division consists of mathematicians, computer specialists, statisticians, biologists, physicians, and social scientists. They collaborate closely with experts from a variety of fields, such as Ministries of Health, and with international organisations like the WHO, UNITAID and the World Bank. The division takes an interdisciplinary approach and combines mathematical modelling (including cost-effectiveness analyses), analyses of cohort data, systematic reviews, text mining, and qualitative research techniques. The division focuses on HIV, influenza and hepatitis, both in Switzerland and abroad. But it is also interested in expanding its work to other infectious diseases, and in studying the interaction between communicable and non-communicable diseases.

(From left to right: Olivia Keiser, Kali Tal, Janne Estill, Barbera Bertisch, Zofia Barańczuk, Maryam Sadeghimer and Matteo Brezzi)

Modelling HIV and HCV Epidemics

Mathematical simulation models to test the effectiveness and cost-effectiveness of different health interventions

We have developed several mathematical simulation models for HIV-infected adults and children, as well as for tuberculosis and hepatitis C. One of our HIV models showed that tracing patients lost to follow-up prevents only a small number of HIV transmissions. In another project, we identified factors that may explain the typical age structure observed among diagnosed tuberculosis patients in Cape Town. To parameterise the models, we analyse primary data and conduct systematic reviews of published literature. We have developed a general version of a disease progression model that can be used for any type of disease; it is avail- able online as an R package. We developed or applied simulation models in many of our other projects.

HIV in Malawi

In Malawi, we evaluated the prevention-of-mother-to-child-transmission program, “Option B+” by combining quantitative and qualitative analyses techniques (see http://www.umoyoplus.org/). In that study, we found that both HIV testing frequency and loss to follow-up varied substantially across sites. When we mapped the data, we realised that loss to follow-up rates clustered spatially. We decided to explore this spatial clustering by analysing data from qualitative focus groups and in-depth interviews of patients and health care workers.

In a follow-up project, we will extend the findings of this study to explore the spatial variability of HIV in Malawi and, wore widely, in sub-Saharan Africa. For this project, we will use state-of-the-art statistical analyses, review qualitative literature on socio-behavioural factors of HIV in Malawi, and develop a spatial simulation model. Since we work closely with local NGOs and the Ministry of Health, our findings will help others to develop and implement locally acceptable interventions.

Other HIV-related collaborations

For the past 10 years, we have led and contributed to many analyses on HIV therapy outcomes in HIV-infected adults and children in sub-Saharan Africa (IeDEA collaboration, www.iedea.org). One of our PhD students is, for example, now working on an analysis of therapy failure and third-line therapy in Zimbabwe. We continue to be an active partner in this worldwide network of HIV cohort studies.

With the groups of Prof David Wilson (Burnet Institute Australia), the World Bank UNAIDS, and other partners, we constitute the “Optima group” (www.optimamodel.com). Optima is an allocative efficiency analysis tool that can be used to inform public health investment choices, and can also be utilised for academic research. The Optima approach involves, for example, assessing the burden of disease over time, defining strategic objectives under logistic, ethical or and/or political constraints; and, determining optimal resources allocation for achieving objectives. Optima is available for HIV, tuberculosis, nutrition, and hepatitis C. Other modules are in development.

Hepatitis C in Switzerland

We have led several epidemiological analyses within the Swiss Hepatitis C Cohort Study SCCS (www.swisshcv.org). We have focused on access to care and therapy outcomes. We also had a mandate from the Swiss Federal Office of Public Health to conduct a situation analysis of hepatitis B and C in Switzerland. We have worked on several simulation models that assess the effect of difference screening and therapy interventions for hepatitis C-infected patients in Switzerland.

Influenza in Switzerland

In collaboration with the Federal Office of Public Health, the virology and infection control departments at the University hospital of Geneva, and other hospitals in Switzerland we are implementing a pilot study for hospitalised influenza cases in Switzerland. It is likely that influenza cases in hospitals differ from community-based cases regarding patient characteristics and potentially also patterns of circulating strains. With a hospital-based system, we will be able to study the evolution of the epidemic and better understand influenza in hospitalised patients who are most at risk.

Olivia Keiser