Produção Nacional
Revisado por pares
Susceptible-infected-recovered and susceptible-exposed-infected models
2011; Institute of Physics; Volume: 44; Issue: 9 Linguagem: Inglês
10.1088/1751-8113/44/9/095005
ISSN1751-8121
AutoresTânia Tomé, Mário J. de Oliveira,
Tópico(s)Evolution and Genetic Dynamics
ResumoTwo stochastic epidemic lattice models, the susceptible-infected-recovered and the susceptible-exposed-infected models, are studied on a Cayley tree of coordination number k. The spreading of the disease in the former is found to occur when the infection probability b is larger than bc = k/2(k − 1). In the latter, which is equivalent to a dynamic site percolation model, the spreading occurs when the infection probability p is greater than pc = 1/(k − 1). We set up and solve the time evolution equations for both models and determine the final and time-dependent properties, including the epidemic curve. We show that the two models are closely related by revealing that their relevant properties are exactly mapped into each other when p = b/[k − (k − 1)b]. These include the cluster size distribution and the density of individuals of each type, quantities that have been determined in closed forms.
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