Critical behavior of a vector-mediated epidemic model

Adriana Dickman

Adriana Gomes Dickman

Catholic University of Minas Gerais, Belo Horizonte, Minas Gerais, Brazil

We study a lattice model for vector-mediated transmission of a disease in a population consisting of two species, A and B, which contract the disease from one another. Individuals of species A are sedentary, while those of species B (the vector) diffuse in space. Examples of such diseases are malaria, dengue fever, and Pierce’s disease in vineyards. There are several ways of interpreting the model: A contact process (CP) on the A population, mediated by B; a diffusive epidemic process (DEP) on the B population, mediated by A; or a multicomponent epidemic process in which B and A are equally essential. The model exhibits a phase transition between an absorbing (infection free) phase and an active one as parameters such as infection rates and vector density are varied. We study the static and dynamic critical behavior of the model using spreading, initial decay, and quasistationary simulations. Although phase transitions to an absorbing state fall generically in the directed percolation (DP) universality class, this appears not to be the case for the present model. Our results clearly exclude DP scaling and strongly suggest DEP universality. They also raise the possibility of two phase transitions in spreading: At the critical point for survival, the number n(t) of infected individuals grows more slowly than a power law, while, for parameters such that n(t) grows as a power law, the survival probability decays more slowly than a power law.


London Mathematical Laboratory, 14 Buckingham Street, London, WC2N 6DF

Date & Time

Wednesday 7th December 2016 at 14.00hrs


LML Seminars are free to attend and no registration is required.