ON AN EPIDEMIC MODEL ON FINITE GRAPHS

Autor(es)

Benjamini, Itai ^[1] ; Fontes, Luiz Renato ^[2] ; Hermon, Jonathan ^[3] ; Machado, Fabio Prates ^[2]

Afiliação do(s) autor(es)

^[1] Weizmann Inst Sci, Dept Math, Rehovot - Israel

^[2] Univ Sao Paulo, Inst Matemat & Estat, Sao Paulo - Brazil

^[3] Univ Cambridge, Dept Pure Math & Math Stat, Cambridge - England

• Tipo de documento: Artigo Científico
• Fonte: ANNALS OF APPLIED PROBABILITY; v. 30, n. 1, p. 208-258, FEB 2020.
• Citações Web of Science: 0

Resumo

We study a system of random walks, known as the frog model, starting from a profile of independent Poisson(lambda) particles per site, with one additional active particle planted at some vertex o of a finite connected simple graph G = (V, E). Initially, only the particles occupying o are active. Active particles perform t is an element of N boolean OR [infinity] steps of the walk they picked before vanishing and activate all inactive particles they hit. This system is often taken as a model for the spread of an epidemic over a population. Let R-t be the set of vertices which are visited by the process, when active particles vanish after t steps. We study the susceptibility of the process on the underlying graph, defined as the random quantity S(G) := inf[t : R-t = V] (essentially, the shortest particles' lifespan required for the entire population to get infected). We consider the cases that the underlying graph is either a regular expander or a d-dimensional torus of side length n (for all d >= 1) T-d(n) and determine the asymptotic behavior of S up to a constant factor. In fact, throughout we allow the particle density lambda to depend on n and for d >= 2 we determine the asymptotic behavior of S(T-d(n)) up to smaller order terms for a wide range of lambda = lambda(n). (AU)

• Processo FAPESP: 17/10555-0 - Modelagem estocástica de sistemas interagentes
• Beneficiário: Fabio Prates Machado
• Modalidade de apoio: Auxílio à Pesquisa - Temático