Speaker: Raquel Lopez

Tittle: Stochasticity in Vaccination

Abstract: Fred Brauer (2004) developed a simple deterministic SIVS model to analyze vaccine effectivity on populations. His model predicted the existence of a backward bifurcation, which means that when the model is started with a sufficiently high number of infected individuals, the disease can persist even if (the mean number of secondary infections caused by a single infective introduced into the susceptible population) R0 < 1. This opposes the fact that if R0 < 1, there is a disease free equilibrium which is asymptotically stable and the disease dies out. Therefore, it is very difficult to control the spread of any infectious disease in the presence of this type of bifurcation. In this work we have considered a stochastic version of Brauers model. We will see how our stochastic model is related to Brauers deterministic model.

Speakers: Danielle Robbins , Daniel Rios-Doria

Title: A Stochastic Model for Cholera Epidemics

Abstract: Cholera is a water borne infectious disease that is endemic in developing regions. In these regions, data shows oscillations in the number of outbreaks, with a larger number of cases occurring during the summer season. Deterministic models have been studied showing the long-term effects of Cholera in a susceptible population do not reflect the oscillations in the data of the endemic case of the disease. The model exhibits damped oscillations around the endemic equilibrium. In this study, we propose a more realistic model by altering the previous model to a stochastic one. This alternate method allowed us to find parameter regimes that reflect sustained oscillatory behavior.

Speaker: Alicia Urdapilleta

Title: Nosocomial Infections R0 a joke!

Abstract: The spread of diseases in hospitals is a considerable problem in many regions of the world. Even in countries with high standards of hygiene, such as Canada, an estimated number of 220,000 infections occur every year, resulting in 8,000 deaths.Forthermore, intra-hospital transfers are very frequent in cities. With the rise of nosocomial infections in hospitals and the patient transfers from hospital to hospital, hospitals are admitting more than just patients. In this study, we wanted to assess the risk of nosocomial infection in these transfered patients. If we have a network of hospitals will the disease be maintained in the individual hospitals or will it spread throughout the network? For network models, the computation of the the basic reproduction number, R0, becomes a challange. However, we are able to find upper and lower bounds for R0 but the bounds are not a good indicator of whether or not the disease will persist or die out. A better indicator of the overall basic reproductive number is an approximation of the R0 for the whole system. We obtained the approximation through an expansion of the next generation matrix. For the numerical simulations we considered a specific network, the star network. This network consists of one central hospital (hub) and five smaller hospitals (leaf). We ran some simulations which suggest that even if the disease is maintained in all hospitals and there is intra-hospital transfers, there is a disease emergence in the network. This suggests the possibility of some backward bifurcation.