Modeling the spread of two successive SIR epidemics on a configuration model network

• We present a stochastic model for two successive SIR (Susceptible, Infectious, Recov-ered) epidemics in the same network structured population. Individuals infected duringthe first epidemic might have (partial) immunity for the second one. The first epidemic isanalysed through a bond percolation model, while the second epidemic is approximated bya three-type branching process in which the types of individuals depend on their position inthe percolation clusters used for the first epidemic. This branching process approximationenables us to calculate a threshold parameter and the probability of a large outbreak for thesecond epidemic.We illustrate our results through two examples. In the first example individuals infectedby the first epidemic are independently either completely susceptible or completely immuneto the second epidemic. The probability of being completely immune is the same for allindividuals infected in the first epidemic. In the second example the recovered individual inthe first epidemic have reduced susceptibility and infectivity for the second epidemic.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

Subsequent SIR epidemics

Reed-Frost model

Percolation

Multi-type branching processes

Mathematical Statistics

matematisk statistik

Publikations- och innehållstyp

vet (ämneskategori)

ovr (ämneskategori)