Stochastic lattice model describing a vector-borne disease

We employ the approach of stochastic dynamics to describe the dissemination of vector-borne diseases such as\ud dengue, and we focus our attention on the characterization of the threshold of the epidemic. The coexistence\ud space comprises two representative spatial structures for both human and mosquito populations. The human\ud population has its evolution described by a process that is similar to the Susceptible-Infected-Recovered (SIR)\ud dynamics. The population of mosquitoes follows a dynamic of the type of the Susceptible Infected-Susceptible\ud (SIS) model. The coexistence space is a bipartite lattice constituted by two structures representing the human\ud and mosquito populations. We develop a truncation scheme to solve the evolution equations for the densities and\ud the two-site correlations from which we get the threshold of the disease and the reproductive ratio. We present\ud a precise deØnition of the reproductive ratio which reveals the importance of the correlations developed in the\ud early stage of the disease. According to our deØnition, the reproductive rate is directed related to the conditional\ud probability of the occurrence of a susceptible human (mosquito) given the presence in the neighborhood of an\ud infected mosquito (human). The threshold of the epidemic as well as the phase transition between the epidemic\ud and the non-epidemic states are also obtained by performing Monte Carlo simulations.\ud References: [1] David R. de Souza, T^ania Tom∂e, , Suani R. T. Pinho, Florisneide R. Barreto and M∂ario J. de\ud Oliveira, Phys. Rev. E 87, 012709 (2013). [2] D. R. de Souza, T. Tom∂e and R. M. ZiÆ, J. Stat. Mech. P03006\ud (2011)

Pair approximation for a model of vertical and horizontal transmission of parasites.

We apply Stochastic Dynamics method for a differential equations model, proposed by Marc Lipsitch and collaborators (Proc. R. Soc. Lond. B 260, 321, 1995), for which the transmission dynamics of parasites occurs from a parent to its offspring (vertical transmission), and by contact with infected host (horizontal transmission). Herpes, Hepatitis and AIDS are examples of diseases for which both horizontal and vertical transmission occur simultaneously during the virus spreading. Understanding the role of each type of transmission in the infection prevalence on a susceptible host population may provide some information about the factors that contribute for the eradication and/or control of those diseases. We present a pair mean-field approximation obtained from the master equation of the model. The pair approximation is formed by the differential equations of the susceptible and infected population densities and the differential equations of pairs that contribute to the former ones. In terms of the model parameters, we obtain the conditions that lead to the disease eradication, and set up the phase diagram based on the local stability analysis of fixed points. We also perform Monte Carlo simulations of the model on complete graphs and Erdös-Rényi graphs in order to investigate the influence of population size and neighborhood on the previous mean-field results; by this way, we also expect to evaluate the contribution of vertical and horizontal transmission on the elimination of parasite. Pair Approximation for a Model of Vertical and Horizontal Transmission of Parasites

Meninas na F´Ä±sica: um desafio para a educa¸c˜ao cient´Ä±fica escolar∗

An overview of the activities of the Commission for Relations and Gender, an organization sponsored by the Brazilian Physical Society, is presented. The focus is on the mainframe of basics action, where the popularization and education in sciences directed to girls in high school is a central activityUma avalia¸c˜ao das atividades da Comiss˜ao de Rela¸c˜oes de Gˆenero da Sociedade Brasileira de F´ísica ´e apresentada. A ˆenfase est´a nos eixos de a¸c˜oes b´asicas, onde se destaca as atividades de divulga¸c˜ao cient´Ä±fica em f´Ä±sica voltadas para as meninas nas escolas

A stochastic spatially structured epidemic model with diffusive processes

We developed a stochastic lattice model to describe the vector-borne disease (like yellow fever or dengue). The model is spatially structured and its dynamical rules take into account the diffusion of vectors. We consider a bipartite lattice, forming a sub-lattice of human and another occupied by mosquitoes. At each site of lattice we associate a stochastic variable that describes the occupation and the health state of a single individual (mosquito or human). The process of disease transmission in the human population follows a similar dynamic of the Susceptible-Infected-Recovered model (SIR), while the disease transmission in the mosquito population has an analogous dynamic of the Susceptible-Infected-Susceptible model (SIS) with mosquitos diffusion. The occurrence of an epidemic is directly related to the conditional probability of occurrence of infected mosquitoes (human) in the presence of susceptible human (mosquitoes) on neighborhood. The probability of diffusion of mosquitoes can facilitate the formation of pairs Susceptible-Infected enabling an increase in the size of the epidemic. Using an asynchronous dynamic update, we study the disease transmission in a population initially formed by susceptible individuals due to the introduction of a single mosquito (human) infected. We find that this model exhibits a continuous phase transition related to the existence or non-existence of an epidemic. By means of mean field approximations and Monte Carlo simulations we investigate the epidemic threshold and the phase diagram in terms of the diffusion probability and the infection probability

Estimation of Tumor Size Evolution Using Particle Filters

Cancer is characterized by the uncontrolled growth of cells with the ability of invading local organs and/or tissues and of spreading to other sites. Several kinds of mathematical models have been proposed in the literature, involving different levels of refinement, for the evolution of tumors and their interactions with chemotherapy drugs. In this article, we present the solution of a state estimation problem for tumor size evolution. A system of nonlinear ordinary differential equations is used as the state evolution model, which involves as state variables the numbers of tumor, normal and angiogenic cells, as well as the masses of the chemotherapy and anti-angiogenic drugs in the body. Measurements of the numbers of tumor and normal cells are considered available for the inverse analysis. Parameters appearing in the formulation of the state evolution model are treated as Gaussian random variables and their uncertainties are taken into account in the estimation of the state variables, by using an algorithm based on the auxiliary sampling importance resampling particle filter. Test cases are examined in the article dealing with a chemotherapy protocol for pancreatic cancer.Indisponível