MSc Math Defence: Optimal Treatment Allocation Under Single-payer Health Care With Pricing Competition

Kevin Fatyas, M.Sc. Defence

Recently announced in the Ontario Budget for 2016, Ontario residents between the ages of 65 and 70 will now be fully covered for the herpes zoster (shingles) virus. This will help some elderly Ontarians avoid paying for treatment, which will have a significant impact on their daily lives. However, most people who suffer from the virus start experiencing symptoms as early as age 50. With a 1-in-3 chance of developing the disease, many Canadians are struggling in their daily lives to cope. Zostavax is currently the only treatment option for shingles on the market at a cost of approximately $170 per dose. Having had no competition, there has been no drive to lower the cost of sale.

In this thesis we use dynamic programming and game theory background to build an optimal allocation model for a known treatment among population groups with a single–payer health care provider (such as Public Health). We model and analyze, using an optimization and game theoretic framework, whether or not the presence of competition may help reduce the cost of vaccines and increase coverage to include more age groups under the same budgetary restrictions. We then show that there are best coverages to be achieved under various budget distributions of two distinct types: one from single-payer to population groups of distinct age, and another from single-payer to producers of treatment. Lastly, we incorporate and discuss a "copay" option for treatment payment such that consumers may be asked to pay up to 10% of the cost of the treatment directly to producers. This is shown to potentially increase the available number of doses to be distributed to the population at the expense of decreased consumer demand as a result of a copay request.