Math Biology Seminar: Judith Bouman

The impact of the annual influenza epidemic is still large; 36,000 deaths in the US each year. Elderly are in particular vulnerable for side effects of an infection. Therefore they need to be protected against getting infected, however, vaccines are less efficient for them. Antiviral treatment can minimize the risk of side-effects, but drug-resistant viruses can appear under treatment. The spread of these resistant type viruses will increase the number of deaths during an epidemic, as vulnerable patients can no longer be treated with the drug.

A mathematical model is used to describe the appearance and spread of drug-resistant viruses during an influenza outbreak in an elderly home. As the appearance of the resistant-viruses happens within a patient under treatment, this is modeled on a within host scale. On the contrary, the spread of resistant type influenza takes place on a between host model and is thus modeled as such. Resistance appears due to a combination of mutations in the viral RNA. Hence, the within host model is stochastic and has to be modeled in that way. However a direct stochastic simulation method would be to time intensive. Therefore, a hybrid simulation method is developed. This method combines a deterministic approach with Gillespie's algorithm. The results of the within host model are used to calculate the probability that an infected person under treatment infects a susceptible with resistant type influenza in the between host model.

The effect of the initial infective, different vaccinating strategies, different treatment times, different treatment rates and a different treatment efficiency function on the epidemic in an elderly home are evaluated. The first conclusion is that the initial infective influences the probability of a major outbreak, but not the distribution of the final size of a major outbreak. Secondly, vaccinating the elderly is more efficient in preventing the spread of resistance than vaccinating health care workers. Thirdly, treatment has to be applied as early as possible and treatment after some time is more harmful than helpful on the long term. Moreover, the treatment rate should be kept as minimal as possible. At last, the treatment efficiency function greatly influences the probability that resistance appears during treatment.