Dynamics of Epidemiological Models

• Type: Article in International Scientific Journal
• Date: 2010

Authors

Alberto Pinto (Author) FCUP; Maira Aguiar (Author) Other; Jose Martins (Author) Other; Nico Stollenwerk (Author) Other

Journal

Title: Acta Biotheoretica

Vol. 58 No. 4

Pages: 381-389

ISSN: 0001-5342

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 8 Citations

Scopus - 9 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-003-08S

DOI: 10.1007/s10441-010-9116-7

Abstract (EN): We study the SIS and SIRI epidemic models discussing different approaches to compute the thresholds that determine the appearance of an epidemic disease. The stochastic SIS model is a well known mathematical model, studied in several contexts. Here, we present recursively derivations of the dynamic equations for all the moments and we derive the stationary states of the state variables using the moment closure method. We observe that the steady states give a good approximation of the quasi-stationary states of the SIS model. We present the relation between the SIS stochastic model and the contact process introducing creation and annihilation operators. For the spatial stochastic epidemic reinfection model SIRI, where susceptibles S can become infected I, then recover and remain only partial immune against reinfection R, we present the phase transition lines using the mean field and the pair approximation for the moments. We use a scaling argument that allow us to determine analytically an explicit formula for the phase transition lines in pair approximation.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 9