## Special Math Biology Seminar HH 410 - Robert Smith? - Unexpected Infection Spikes in a Model of Respiratory Syncytial Virus Vaccination

### Description

**HH410**

Speaker: Dr. Robert Smith? (University of Ottawa)

Title: Unexpected Infection Spikes in a Model of Respiratory Syncytial Virus

Vaccination

Abstract:

Respiratory Syncytial Virus (RSV) is an acute respiratory infection

that infects millions of children and infants worldwide. Recent research has

shown promise for the development of a vaccine, with a range of vaccine types

now in clinical trials or preclinical development. We extend an existing

mathematical model with seasonal transmission to include vaccination. We model

vaccination both as a continuous process, applying the vaccine during pregnancy,

and as a discrete one, using impulsive differential equations, applying pulse

vaccination. We develop conditions for the stability of the disease-free

equilibrium and show that this equilibrium can be destabilized under certain

extreme conditions, even with 100% coverage using an (unrealistic) vaccine.

Using impulsive differential equations and introducing a new quantity, the

impulsive reproduction number, we showed that eradication could be achieved with

75% coverage, while 50% coverage resulted in low-level oscillations. A vaccine

that targets RSV infection has the potential to significantly reduce the overall

prevalence of the disease, but appropriate coverage is critical.

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