Equilibrium properties of the spatial SIS model as a point pattern dynamics - How is infection distributed over space?. (7th May 2019)

• Record Type: Journal Article
• Authors: Hamada, Miki; Takasu, Fugo
• Is Part Of: Journal of theoretical biology. Volume 468(2019)
• Page Start: 12
• Page End: 26
• Publication Date: 2019-05-07
• Subjects: Epidemiology -- Distance-dependent interactions -- Spatial population dynamics -- Spatial ecology; Biology -- Periodicals; Biological Science Disciplines -- Periodicals; Biology -- Periodicals; Biologie -- Périodiques; Theoretische biologie; Biology; Periodicals; 571.05
• DOI: 10.1016/j.jtbi.2019.02.005
• Languages: English
• ISSNs: 0022-5193

Abstract

Highlights: We analyze the SIS stochastic point pattern dynamics in terms of singlets and pairs. Equilibrium singlets and pair probabilities are analytically derived. Infectious points are spatially clustered in the order of the infection kernel. Infection kernel could be estimated from the 2nd order structure of point pattern. Abstract: We revisit the classical epidemiological SIS model as a stochastic point pattern dynamics with special focus on its spatial distribution at equilibrium. In this model, each point on a continuous space is either susceptible S or infectious I, and infection occurs with an infection kernel as a function of distance from I to S . This stochastic process has been mathematically described by the hierarchical dynamics of the probabilities that a point, a pair made by two points, and a triplet made by three points, etc., is in a specific configuration of status. Using a simple closure thereby triplet probabilities that appear in the dynamics are approximated, we show that the average singlet probabilities and the pair probabilities that describe spatial distributions of S s and I s at equilibrium can be explicitly derived using the infection kernel; I s are spatially clustered in the same order of the infection kernel. The results highlight the advantage of point pattern approach to model spatial population dynamics in general ecology where local interactions among individuals likely depend on distance between them.