Bulletin of Mathematical Biology

, Volume 68, Issue 2, pp 401–416

# A Model of Spatial Epidemic Spread When Individuals Move Within Overlapping Home Ranges

• Timothy C. Reluga
• Jan Medlock
• Alison P. Galvani
Original Article

DOI: 10.1007/s11538-005-9027-y

Reluga, T.C., Medlock, J. & Galvani, A.P. Bull. Math. Biol. (2006) 68: 401. doi:10.1007/s11538-005-9027-y

## Abstract

One of the central goals of mathematical epidemiology is to predict disease transmission patterns in populations. Two models are commonly used to predict spatial spread of a disease. The first is the distributed-contacts model, often described by a contact distribution among stationary individuals. The second is the distributed-infectives model, often described by the diffusion of infected individuals. However, neither approach is ideal when individuals move within home ranges. This paper presents a unified modeling hypothesis, called the restricted-movement model. We use this model to predict spatial spread in settings where infected individuals move within overlapping home ranges. Using mathematical and computational approaches, we show that our restricted-movement model has three limits: the distributed-contacts model, the distributed-infectives model, and a third, less studied advective distributed-infectives limit. We also calculate approximate upper bounds for the rates of an epidemic's spatial spread. Guidelines are suggested for determining which limit is most appropriate for a specific disease.

### Keywords

Epidemics Invasions Distributed-contacts Distributed-infectives

© Society for Mathematical Biology 2006

## Authors and Affiliations

• Timothy C. Reluga
• 1
• Jan Medlock
• 1
• Alison P. Galvani
• 1
1. 1.Department of Epidemiology and Public HealthYale University School of MedicineNew HavenUS