title: Efficient method for comprehensive computation of agent-level epidemic dissemination in networks.
abstract: Susceptible-infected (SI) and susceptible-infected-susceptible (SIS) are simple agent-based models often employed in epidemic studies. Both models describe the time evolution of infectious diseases in networks whose vertices are either susceptible (S) or infected (I) agents. Precise estimation for disease spreading is one of the major goals in epidemic studies but often restricted to heavy numerical simulations. Analytic methods using operatorial content are subject to the asymmetric eigenvalue problem, limiting the use of perturbative methods. Numerical methods are limited to small populations, since the vector space increases exponentially with population size N. Here, we propose the use of the squared norm of the probability vector to obtain an algebraic equation, which permits the evaluation of stationary states in Markov processes. The equation requires the eigenvalues of symmetrized time generators and takes full advantage of symmetries, reducing the time evolution to an O(N) sparse problem. The calculation of eigenvalues employs quantum many-body techniques, while the standard perturbation theory accounts for small modifications to the network topology.
authors.affiliation: Universidade de São Paulo (USP), Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP), Av. Bandeirantes 3900, Ribeirão Preto 14040-901, Brazil.
authors.forename: Gilberto M
authors.initials: GM
authors.lastname: Nakamura
authors.affiliation: Universidade de São Paulo (USP), Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP), Av. Bandeirantes 3900, Ribeirão Preto 14040-901, Brazil.
authors.forename: Ana Carolina P
authors.initials: AC
authors.lastname: Monteiro
authors.affiliation: Universidade de São Paulo (USP), Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP), Av. Bandeirantes 3900, Ribeirão Preto 14040-901, Brazil.
authors.forename: George C
authors.initials: GC
authors.lastname: Cardoso
authors.affiliation: Universidade de São Paulo (USP), Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP), Av. Bandeirantes 3900, Ribeirão Preto 14040-901, Brazil.|Instituto Nacional de Ciência e Tecnologia - Sistemas Complexos (INCT-SC), Rio de Janeiro 22460-320, Brazil.
authors.forename: Alexandre S
authors.initials: AS
authors.lastname: Martinez
mesh_terms: D000465:Algorithms; D003141:Communicable Diseases / Q000453:epidemiology*; D004198:Disease Susceptibility / Q000453:epidemiology*; D058872:Epidemics / Q000706:statistics & numerical data*; D006801:Humans; D008390:Markov Chains; D008962:Models, Theoretical; D011336:Probability