A new scale-invariant ratio and finite-size scaling for the stochastic susceptible-infected-recovered model

The critical behavior of the stochastic susceptible-infected-recovered model on a square lattice is obtained by numerical simulations and finite-size scaling. The order parameter as well as the distribution in the number of recovered individuals is determined as a function of the infection rate for several values of the system size. The analysis around criticality is obtained by exploring the close relationship between the present model and standard percolation theory. The quantity UP, equal to the ratio U between the second moment and the squared first moment of the size distribution multiplied by the order parameter P, is shown to have, for a square system, a universal value 1.0167(1) that is the same for site and bond percolation, confirming further that the SIR model is also in the percolation class.

Bayesian estimation of the dynamics of pandemic (H1N1) 2009 influenza transmission in Queensland: A space–time SIR-based model

Background A pandemic strain of influenza A spread rapidly around the world in 2009, now referred to as pandemic (H1N1) 2009. This study aimed to examine the spatiotemporal variation in the transmission rate of pandemic (H1N1) 2009 associated with changes in local socio-environmental conditions from May 7–December 31, 2009, at a postal area level in Queensland, Australia. Method We used the data on laboratory-confirmed H1N1 cases to examine the spatiotemporal dynamics of transmission using a flexible Bayesian, space–time, Susceptible-Infected-Recovered (SIR) modelling approach. The model incorporated parameters describing spatiotemporal variation in H1N1 infection and local socio-environmental factors. Results The weekly transmission rate of pandemic (H1N1) 2009 was negatively associated with the weekly area-mean maximum temperature at a lag of 1 week (LMXT) (posterior mean: −0.341; 95% credible interval (CI): −0.370–−0.311) and the socio-economic index for area (SEIFA) (posterior mean: −0.003; 95% CI: −0.004–−0.001), and was positively associated with the product of LMXT and the weekly area-mean vapour pressure at a lag of 1 week (LVAP) (posterior mean: 0.008; 95% CI: 0.007–0.009). There was substantial spatiotemporal variation in transmission rate of pandemic (H1N1) 2009 across Queensland over the epidemic period. High random effects of estimated transmission rates were apparent in remote areas and some postal areas with higher proportion of indigenous populations and smaller overall populations. Conclusions Local SEIFA and local atmospheric conditions were associated with the transmission rate of pandemic (H1N1) 2009. The more populated regions displayed consistent and synchronized epidemics with low average transmission rates. The less populated regions had high average transmission rates with more variations during the H1N1 epidemic period.

Accelerating Information Diffusion in Social Networks Under the Susceptible-Infected-Susceptible Epidemic Model

Standard Susceptible-Infected-Susceptible (SIS) epidemic models assume that a message spreads from the infected to the susceptible nodes due to only susceptible-infected epidemic contact. We modify the standard SIS epidemic model to include direct recruitment of susceptible individuals to the infected class at a constant rate (independent of epidemic contacts), to accelerate information spreading in a social network. Such recruitment can be carried out by placing advertisements in the media. We provide a closed form analytical solution for system evolution in the proposed model and use it to study campaigning in two different scenarios. In the first, the net cost function is a linear combination of the reward due to extent of information diffusion and the cost due to application of control. In the second, the campaign budget is fixed. Results reveal the effectiveness of the proposed system in accelerating and improving the extent of information diffusion. Our work is useful for devising effective strategies for product marketing and political/social-awareness/crowd-funding campaigns that target individuals in a social network.

Explaining the high number of infected people by dengue in Rio de Janeiro in 2008 using a susceptible-infective-recovered model

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Susceptible-infected-recovered and susceptible-exposed-infected models

Two 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 b(c) = 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 p(c) = 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.

Modelos matemáticos em epidemiologia

Pós-graduação em Matemática Universitária - IGCE

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.

Household epidemic models with varying infection response

This paper is concerned with SIR (susceptible--infected--removed) household epidemic models in which the infection response may be either mild or severe, with the type of response also affecting the infectiousness of an individual. Two different models are analysed. In the first model, the infection status of an individual is predetermined, perhaps due to partial immunity, and in the second, the infection status of an individual depends on the infection status of its infector and on whether the individual was infected by a within- or between-household contact. The first scenario may be modelled using a multitype household epidemic model, and the second scenario by a model we denote by the infector-dependent-severity household epidemic model. Large population results of the two models are derived, with the focus being on the distribution of the total numbers of mild and severe cases in a typical household, of any given size, in the event that the epidemic becomes established. The aim of the paper is to investigate whether it is possible to determine which of the two underlying explanations is causing the varying response when given final size household outbreak data containing mild and severe cases. We conduct numerical studies which show that, given data on sufficiently many households, it is generally possible to discriminate between the two models by comparing the Kullback-Leibler divergence for the two fitted models to these data.

Analysis of a stochastic SIR epidemic on a random network incorporating household structure

This paper is concerned with a stochastic SIR (susceptible-infective-removed) model for the spread of an epidemic amongst a population of individuals, with a random network of social contacts, that is also partitioned into households. The behaviour of the model as the population size tends to infinity in an appropriate fashion is investigated. A threshold parameter which determines whether or not an epidemic with few initial infectives can become established and lead to a major outbreak is obtained, as are the probability that a major outbreak occurs and the expected proportion of the population that are ultimately infected by such an outbreak, together with methods for calculating these quantities. Monte Carlo simulations demonstrate that these asymptotic quantities accurately reflect the behaviour of finite populations, even for only moderately sized finite populations. The model is compared and contrasted with related models previously studied in the literature. The effects of the amount of clustering present in the overall population structure and the infectious period distribution on the outcomes of the model are also explored.

Identifying influential nodes in complex networks: A multiple attributes fusion method

How to identify influential nodes is still an open hot issue in complex networks. Lots of methods (e.g., degree centrality, betweenness centrality or K-shell) are based on the topology of a network. These methods work well in scale-free networks. In order to design a universal method suitable for networks with different topologies, this paper proposes a Multiple Attribute Fusion (MAF) method through combining topological attributes and diffused attributes of a node together. Two fusion strategies have been proposed in this paper. One is based on the attribute union (FU), and the other is based on the attribute ranking (FR). Simulation results in the Susceptible-Infected (SI) model show that our proposed method gains more information propagation efficiency in different types of networks. © 2014 Springer International Publishing.

Complexity and anisotropy in host morphology make populations less susceptible to epidemic outbreaks

One of the challenges in epidemiology is to account for the complex morphological structure of hosts such as plant roots, crop fields, farms, cells, animal habitats and social networks, when the transmission of infection occurs between contiguous hosts. Morphological complexity brings an inherent heterogeneity in populations and affects the dynamics of pathogen spread in such systems. We have analysed the influence of realistically complex host morphology on the threshold for invasion and epidemic outbreak in an SIR (susceptible-infected-recovered) epidemiological model. We show that disorder expressed in the host morphology and anisotropy reduces the probability of epidemic outbreak and thus makes the system more resistant to epidemic outbreaks. We obtain general analytical estimates for minimally safe bounds for an invasion threshold and then illustrate their validity by considering an example of host data for branching hosts (salamander retinal ganglion cells). Several spatial arrangements of hosts with different degrees of heterogeneity have been considered in order to separately analyse the role of shape complexity and anisotropy in the host population. The estimates for invasion threshold are linked to morphological characteristics of the hosts that can be used for determining the threshold for invasion in practical applications.

A disease evolution model with uncertain parameters

In this study we consider the SIS epidemiological model (susceptible-infected-susceptible) in which the transmission and recuperation rates are considered fuzzy sets. The concepts of possibility measures and fuzzy expectancy value are used to obtain the basic reproduction value for infected groups with different viral charge.

Antimicrobial activity of triantibiotic paste, 2% chlorhexidine gel, and calcium hydroxide on an intraoral-infected dentin biofilm model

Introduction: The purpose of this study was to evaluate the antimicrobial activity of calcium hydroxide, 2% chlorhexidine gel, and triantibiotic paste (ie, metronidazole, minocycline, and ciprofloxacin) by using an intraorally infected dentin biofilm model. Methods: Forty bovine dentin specimens were infected intraorally using a removable orthodontic device in order to induce the biofilm colonization of the dentin. Then, the samples were treated with the medications for 7 days. Saline solution was used as the control. Two evaluations were performed: immediately after the elimination of the medication and after incubation in brain-heart infusion medium for 24 hours. The Live/Dead technique (Invitrogen, Eugene, OR) and a confocal microscope were used to obtain the percentage of live cells. Nonparametric statistical tests were performed to show differences in the percentage of live cells among the groups (P < .05). Results: Calcium hydroxide and 2% chlorhexidine gel did not show statistical differences in the immediate evaluation. However, after application of the brain-heart infusion medium for 24 hours, 2% gel chlorhexidine showed a statistically lesser percentage of live cells in comparison with calcium hydroxide. The triantibiotic paste significantly showed a lower percentage of live cells in comparison with the 2% chlorhexidine gel and calcium hydroxide groups in the immediate and secondary (after 24 hours) evaluations. Conclusions: The triantibiotic paste was most effective at killing the bacteria in the biofilms on the intraorally infected dentin model in comparison with 2% chlorhexidine gel and calcium hydroxide

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

Tuberculosis in Cape Town: An age-structured transmission model.

BACKGROUND Tuberculosis (TB) is the leading cause of death in South Africa. The burden of disease varies by age, with peaks in TB notification rates in the HIV-negative population at ages 0-5, 20-24, and 45-49 years. There is little variation between age groups in the rates in the HIV-positive population. The drivers of this age pattern remain unknown. METHODS We developed an age-structured simulation model of Mycobacterium tuberculosis (Mtb) transmission in Cape Town, South Africa. We considered five states of TB progression: susceptible, infected (latent TB), active TB, treated TB, and treatment default. Latently infected individuals could be re-infected; a previous Mtb infection slowed progression to active disease. We further considered three states of HIV progression: HIV negative, HIV positive, on antiretroviral therapy. To parameterize the model, we analysed treatment outcomes from the Cape Town electronic TB register, social mixing patterns from a Cape Town community and used literature estimates for other parameters. To investigate the main drivers behind the age patterns, we conducted sensitivity analyses on all parameters related to the age structure. RESULTS The model replicated the age patterns in HIV-negative TB notification rates of Cape Town in 2009. Simulated TB notification rate in HIV-negative patients was 1000/100,000 person-years (pyrs) in children aged <5 years and decreased to 51/100,000 in children 5-15 years. The peak in early adulthood occurred at 25-29 years (463/100,000 pyrs). After a subsequent decline, simulated TB notification rates gradually increased from the age of 30 years. Sensitivity analyses showed that the dip after the early adult peak was due to the protective effect of latent TB and that retreatment TB was mainly responsible for the rise in TB notification rates from the age of 30 years. CONCLUSION The protective effect of a first latent infection on subsequent infections and the faster progression in previously treated patients are the key determinants of the age-structure of TB notification rates in Cape Town.