SIR model with local and global infective contacts. A deterministic approach and applications.

MALTZ, A.; FABRICIUS, G.

THEORETICAL POPULATION BIOLOGY

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: Amsterdam; Año: 2016 vol. 112 p. 70 - 79

0040-5809

Abstract: An epidemic model with births and deaths is considered on atwo-dimensional LxL lattice. Each individual can have global infectivecontacts according to the standard susceptible-infected-recovered (SIR)model rules or local infective contacts with their nearest neighbors. Wepropose a deterministic approach to this model and, for the parameterscorresponding to pertussis and rubella in the prevaccine era, verify thatthere is a close agreement with the stochastic simulations when epidemicspread or endemic stationarity is considered. We also find that ourapproach captures the characteristic features of the dynamic behavior ofthe system after a sudden decrease in global contacts that may arise as aconsequence of health care measures. By using the deterministic approach,we are able to characterize the exponential growth of the epidemicbehavior and analyze the stability of the system at the stationaryvalues. Since the deterministic approximation captures the essentialfeatures of the disease transmission dynamics of the stochastic model,itprovides a useful tool for performing systematic studies as a function ofthe model parameters. We give an example of this potentiality byanalyzing the likelihood of the endemic state to become extinct when theweight of the global contacts is drastically reduced.