Stochastic Dynamics of Biological Poupulations

Author(s)

Flávia Mayumi Ruziska Hirata

• Document type: Doctoral Thesis
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Física (IF/SBI)
• Defense date: 2017-08-15

Examining board members

Tania Tome Martins de Castro; Jeferson Jacob Arenzon; Masayuki Oka Hase; Suani Tavares Rubim de Pinho; Silvio Roberto de Azevedo Salinas

• Advisor: Tania Tome Martins de Castro

Abstract

In this thesis we investigate irreversible models within the context of nonequilibrium statistical mechanics motivated by some problems of biological population dynamics. We look for dentifying the existence of phase transition and the universality classes to which the models belong. In addition to that, we look for models that capture the main characteristics of the biological systems which we are interested in describing. We found the exact analytic solution of the susceptible-infected-recovered (SIR) model on one-dimensional lattice. We investigated the susceptible-infected-recovered model with recurrent infection. We showed that the model belongs to the isotropic percolation universality class, except for the parameters that make the model become a contact process. We obtained the transition line between the phases in which there is propagation of the epidemic and in which there is not, by means of mean-field approximations and Monte Carlo simulations on a square lattice. Furthermore, we investigated a dynamic for two biological species and ecological niches; for this purpose we introduced an irreversible stochastic model with four states. We conclude that the modoffers a description of time oscillations of the species populations and of the alternating dominance between them. To achieve this conclusion we used Monte Carlo simulations of this model on a square lattice, mean-field approximation, and the birth and death master equation approach, which for large populations can be approximated by a Fokker-Planck equation that is associated to a set of Langevin equations. Finally, using Monte Carlo simulations, we analyzed a dynamic for two biological species and ecological niches including diffusion. Again, we verified that the model generates scenarios with time oscillations of the species populations and with alternating dominance between them. Also, we conclude that the model belongs to the directed percolation universality class and we found the phase diagram. (AU)

• FAPESP's process: 12/22929-9 - Stochastic dynamics of biological populations
• Grantee: Flávia Mayumi Ruziska Hirata
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)