Dynamics of a childhood disease model with isolation

Joan Ponce

Purdue University

Abstract: One of the main challenges of mathematical modeling is the balance between simplifying assumptions and incorporating sufficient complexity for the model to provide more accurate and reliable outcomes. For mathematical simplicity, many commonly used epidemiological models make restrictive modeling assumptions. Although models under such assumptions are capable of producing useful insights into the biological questions in many cases, they may generate discrepancies in model outcomes. One of the common assumptions in infectious disease models is that the duration for disease stages is exponentially distributed. This may result in discrepancies in model outcomes between such a model and models with more realistic stage distribution assumptions such as gamma distributions with the shape parameter greater than one (Feng et al., 2007). In this talk, I will present an ODE model with gamma-distributed infectious and isolated periods and compare it with a model with exponentially distributed stages. These models intend to show that, for childhood diseases, isolation of infected children may be a possible mechanism responsible for the observed oscillatory behavior in incidence. This is shown analytically by identifying a Hopf bifurcation with the isolation period as the bifurcation parameter.

An important result is that the threshold value for isolation to generate sustained oscillations from the model with gamma-distributed isolation period is much more realistic than the model assuming exponential distributions.

About the speaker:  Joan Ponce is a graduate student from Purdue University