RUMOR PROCESSES ON N

We study four discrete-time stochastic systems on N, modeling processes of rumor spreading. The involved individuals can either have an active or a passive role, speaking up or asking for the rumor. The appetite for spreading or hearing the rumor is represented by a set of random variables whose distributions may depend on the individuals. Our goal is to understand-based on the distribution of the random variables-whether the probability of having an infinite set of individuals knowing the rumor is positive or not.

NONHOMOGENEOUS RANDOM WALKS SYSTEMS ON Z

We consider a random walks system on Z in which each active particle performs a nearest-neighbor random walk and activates all inactive particles it encounters. The movement of an active particle stops when it reaches a certain number of jumps without activating any particle. We prove that if the process relies on efficient particles (i.e. those particles with a small probability of jumping to the left) being placed strategically on Z, then it might survive, having active particles at any time with positive probability. On the other hand, we may construct a process that dies out eventually almost surely, even if it relies on efficient particles. That is, we discuss what happens if particles are initially placed very far away from each other or if their probability of jumping to the right tends to I but not fast enough.

Especulação sobre a taxa de infecção da difteria no Modelo Estocástico Simples de Epidemia

Com base em um programa em linguagem Fortran, utilizando a técnica de simulação em computador e através das pressuposições do Modelo Estocástico Simples de Epidemia, é estabelecida uma conjectura a respeito de valores para a taxa de infecção para a difteria, a partir de ocorrência de casos em um domicílio de cinco pessoas.

Basic ingredients for mathematical modeling of tumor growth in vitro: Cooperative effects and search for space

Based on the literature data from HT-29 cell monolayers, we develop a model for its growth, analogous to an epidemic model, mixing local and global interactions. First, we propose and solve a deterministic equation for the progress of these colonies. Thus, we add a stochastic (local) interaction and simulate the evolution of an Eden-like aggregate by using dynamical Monte Carlo methods. The growth curves of both deterministic and stochastic models are in excellent agreement with the experimental observations. The waiting times distributions, generated via our stochastic model, allowed us to analyze the role of mesoscopic events. We obtain log-normal distributions in the initial stages of the growth and Gaussians at long times. We interpret these outcomes in the light of cellular division events: in the early stages, the phenomena are dependent each other in a multiplicative geometric-based process, and they are independent at long times. We conclude that the main ingredients for a good minimalist model of tumor growth, at mesoscopic level, are intrinsic cooperative mechanisms and competitive search for space. © 2013 Elsevier Ltd.

Modeling the emergence of HIV-1 drug resistance resulting from antiretroviral therapy: Insights from theoretical and numerical studies

The use of antiretroviral therapy has proven to be remarkably effective in controlling the progression of human immunodeficiency virus (HIV) infection and prolonging patient's survival. Therapy however may fail and therefore these benefits can be compromised by the emergence of HIV strains that are resistant to the therapy. In view of these facts, the question of finding the reason for which drug-resistant strains emerge during therapy has become a worldwide problem of great interest. This paper presents a deterministic HIV-1 model to examine the mechanisms underlying the emergence of drug-resistance during therapy. The aim of this study is to determine whether, and how fast, antiretroviral therapy may determine the emergence of drug resistance by calculating the basic reproductive numbers. The existence, feasibility and local stability of the equilibriums are also analyzed. By performing numerical simulations we show that Hopf bifurcation may occur. The model suggests that the individuals with drug-resistant infection may play an important role in the epidemic of HIV. (C) 2011 Elsevier Ireland Ltd. All rights reserved.

Estimates of global, regional, and national incidence, prevalence, and mortality of HIV, 1980-2015 : the Global Burden of Disease Study 2015

Background Timely assessment of the burden of HIV/AIDS is essential for policy setting and programme evaluation. In this report from the Global Burden of Disease Study 2015 (GBD 2015), we provide national estimates of levels and trends of HIV/AIDS incidence, prevalence, coverage of antiretroviral therapy (ART), and mortality for 195 countries and territories from 1980 to 2015. Methods For countries without high-quality vital registration data, we estimated prevalence and incidence with data from antenatal care clinics and population-based seroprevalence surveys, and with assumptions by age and sex on initial CD4 distribution at infection, CD4 progression rates (probability of progression from higher to lower CD4 cell-count category), on and off antiretroviral therapy (ART) mortality, and mortality from all other causes. Our estimation strategy links the GBD 2015 assessment of all-cause mortality and estimation of incidence and prevalence so that for each draw from the uncertainty distribution all assumptions used in each step are internally consistent. We estimated incidence, prevalence, and death with GBD versions of the Estimation and Projection Package (EPP) and Spectrum software originally developed by the Joint United Nations Programme on HIV/AIDS (UNAIDS). We used an open-source version of EPP and recoded Spectrum for speed, and used updated assumptions from systematic reviews of the literature and GBD demographic data. For countries with high-quality vital registration data, we developed the cohort incidence bias adjustment model to estimate HIV incidence and prevalence largely from the number of deaths caused by HIV recorded in cause-of-death statistics. We corrected these statistics for garbage coding and HIV misclassifi cation. Findings Global HIV incidence reached its peak in 1997, at 3·3 million new infections (95% uncertainty interval [UI] 3·1–3·4 million). Annual incidence has stayed relatively constant at about 2·6 million per year (range 2·5–2·8 million) since 2005, after a period of fast decline between 1997 and 2005. The number of people living with HIV/AIDS has been steadily increasing and reached 38·8 million (95% UI 37·6–40·4 million) in 2015. At the same time, HIV/AIDS mortality has been declining at a steady pace, from a peak of 1·8 million deaths (95% UI 1·7–1·9 million) in 2005, to 1·2 million deaths (1·1–1·3 million) in 2015. We recorded substantial heterogeneity in the levels and trends of HIV/AIDS across countries. Although many countries have experienced decreases in HIV/AIDS mortality and in annual new infections, other countries have had slowdowns or increases in rates of change in annual new infections. Interpretation Scale-up of ART and prevention of mother-to-child transmission has been one of the great successes of global health in the past two decades. However, in the past decade, progress in reducing new infections has been slow, development assistance for health devoted to HIV has stagnated, and resources for health in low-income countries have grown slowly. Achievement of the new ambitious goals for HIV enshrined in Sustainable Development Goal 3 and the 90-90-90 UNAIDS targets will be challenging, and will need continued eff orts from governments and international agencies in the next 15 years to end AIDS by 2030.

Developing an epidemic forecasting model for Influenza A in Brisbane, Australia, based on climate and Hong Kong Influenza A surveillance data

Influenza is associated with substantial disease burden [ 1]. Development of a climate-based early warning system for in fluenza epidemics has been recommended given the signi fi - cant association between climate variability and influenza activity [2]. Brisbane is a subtropical city in Australia and offers free in fluenza vaccines to residents aged ≥65 years considering their high risks in developing life-threatening complications, especially for in fluenza A predominant seasons. Hong Kong is an international subtropical city in Eastern Asia and plays a crucial role in global infectious diseases transmission dynamics via the international air transportation network [3, 4]. We hypothesized that Hong Kong in fluenza surveillance data could provide a signal for in fluenza epidemics in Brisbane [ 4]. This study aims to develop an epidemic forecasting model for influenza A in Brisbane elders, by combining climate variability and Hong Kong in fluenza A surveillance data. Weekly numbers of laboratoryconfirmed influenza A positive isolates for people aged ≥65 years from 2004 to 2009 were obtained for Brisbane from Queensland Health, Australia, and for Hong Kong from Queen Mary Hospital (QMH). QMH is the largest public hospital located in Hong Kong Island, and in fluenza surveillance data from this hospital have been demonstrated to be representative for influenza circulation in the entirety of Hong Kong [ 5]. The Brisbane in fluenza A epidemics occurred during July –September, whereas the Hong Kong in fluenza A epidemics occurred during February –March and May –August.

Stochastic lattice gas model describing the dynamics of the SIRS epidemic process

We study a stochastic process describing the onset of spreading dynamics of an epidemic in a population composed of individuals of three classes: susceptible (S), infected (I), and recovered (R). The stochastic process is defined by local rules and involves the following cyclic process: S -> I -> R -> S (SIRS). The open process S -> I -> R (SIR) is studied as a particular case of the SIRS process. The epidemic process is analyzed at different levels of description: by a stochastic lattice gas model and by a birth and death process. By means of Monte Carlo simulations and dynamical mean-field approximations we show that the SIRS stochastic lattice gas model exhibit a line of critical points separating the two phases: an absorbing phase where the lattice is completely full of S individuals and an active phase where S, I and R individuals coexist, which may or may not present population cycles. The critical line, that corresponds to the onset of epidemic spreading, is shown to belong in the directed percolation universality class. By considering the birth and death process we analyze the role of noise in stabilizing the oscillations. (C) 2009 Elsevier B.V. All rights reserved.

Stability and sensitivity analysis of Be-CoDiS, an epidemiological model to predict the spread of human diseases between countries. Validation with data from the 2014-16 West African Ebola Virus Disease epidemic.

Ebola virus disease is a lethal human and primate disease that requires a particular attention from the international health authorities due to important recent outbreaks in some Western African countries and isolated cases in European and North-America continents. Regarding the emergency of this situation, various decision tools, such as mathematical models, were developed to assist the authorities to focus their efforts in important factors to eradicate Ebola. In a previous work, we have proposed an original deterministic spatial-temporal model, called Be-CoDiS (Between-Countries Disease Spread), to study the evolution of human diseases within and between countries by taking into consideration the movement of people between geographical areas. This model was validated by considering numerical experiments regarding the 2014-16 West African Ebola Virus Disease epidemic. In this article, we propose to perform a stability analysis of Be-CoDiS. Our first objective is to study the equilibrium states of simplified versions of this model, limited to the cases of one an two countries, and to determine their basic reproduction ratios. Then, in order to give some recommendations for the allocation of resources used to control the disease, we perform a sensitivity analysis of those basic reproduction ratios regarding the model parameters. Finally, we validate the obtained results by considering numerical experiments based on data from the 2014-16 West African Ebola Virus Disease epidemic.

Dengue fever and el nino-southern oscillation in Queensland, Australia : a time series predictive model

Background It remains unclear over whether it is possible to develop an epidemic forecasting model for transmission of dengue fever in Queensland, Australia. Objectives To examine the potential impact of El Niño/Southern Oscillation on the transmission of dengue fever in Queensland, Australia and explore the possibility of developing a forecast model of dengue fever. Methods Data on the Southern Oscillation Index (SOI), an indicator of El Niño/Southern Oscillation activity, were obtained from the Australian Bureau of Meteorology. Numbers of dengue fever cases notified and the numbers of postcode areas with dengue fever cases between January 1993 and December 2005 were obtained from the Queensland Health and relevant population data were obtained from the Australia Bureau of Statistics. A multivariate Seasonal Auto-regressive Integrated Moving Average model was developed and validated by dividing the data file into two datasets: the data from January 1993 to December 2003 were used to construct a model and those from January 2004 to December 2005 were used to validate it. Results A decrease in the average SOI (ie, warmer conditions) during the preceding 3–12 months was significantly associated with an increase in the monthly numbers of postcode areas with dengue fever cases (β=−0.038; p = 0.019). Predicted values from the Seasonal Auto-regressive Integrated Moving Average model were consistent with the observed values in the validation dataset (root-mean-square percentage error: 1.93%). Conclusions Climate variability is directly and/or indirectly associated with dengue transmission and the development of an SOI-based epidemic forecasting system is possible for dengue fever in Queensland, Australia.

Risk factor analysis and spatiotemporal CART model of cryptosporidiosis in Queensland, Australia

Background: It remains unclear whether it is possible to develop a spatiotemporal epidemic prediction model for cryptosporidiosis disease. This paper examined the impact of social economic and weather factors on cryptosporidiosis and explored the possibility of developing such a model using social economic and weather data in Queensland, Australia. ----- ----- Methods: Data on weather variables, notified cryptosporidiosis cases and social economic factors in Queensland were supplied by the Australian Bureau of Meteorology, Queensland Department of Health, and Australian Bureau of Statistics, respectively. Three-stage spatiotemporal classification and regression tree (CART) models were developed to examine the association between social economic and weather factors and monthly incidence of cryptosporidiosis in Queensland, Australia. The spatiotemporal CART model was used for predicting the outbreak of cryptosporidiosis in Queensland, Australia. ----- ----- Results: The results of the classification tree model (with incidence rates defined as binary presence/absence) showed that there was an 87% chance of an occurrence of cryptosporidiosis in a local government area (LGA) if the socio-economic index for the area (SEIFA) exceeded 1021, while the results of regression tree model (based on non-zero incidence rates) show when SEIFA was between 892 and 945, and temperature exceeded 32°C, the relative risk (RR) of cryptosporidiosis was 3.9 (mean morbidity: 390.6/100,000, standard deviation (SD): 310.5), compared to monthly average incidence of cryptosporidiosis. When SEIFA was less than 892 the RR of cryptosporidiosis was 4.3 (mean morbidity: 426.8/100,000, SD: 319.2). A prediction map for the cryptosporidiosis outbreak was made according to the outputs of spatiotemporal CART models. ----- ----- Conclusions: The results of this study suggest that spatiotemporal CART models based on social economic and weather variables can be used for predicting the outbreak of cryptosporidiosis in Queensland, Australia.

A potential HIV epidemic among male street laborers in urban Vietnam

Background: Mass migration to Asian cities is a defining phenomenon of the present age, as hundreds of millions of people move from rural areas or between cities in search of economic prosperity. Although many do prosper, large numbers of people experience significant social disadvantage. This is especially the case among poorly educated, migrant unskilled unregistered male laborers who do much of the manual work throughout the cities. These men are at significant risk for many health problems, including HIV infection. However, to date there has been little research in developing countries to explain the determinants of this risk, and thereby to suggest feasible preventive strategies. Objectives and Methodology: Using combined qualitative and quantitative methods, the aim of this study was to explore the social contexts that affect health vulnerabilities and to develop conceptual models to predict risk behaviors for HIV [illicit drug use, unsafe sex, and non-testing for HIV] among male street laborers in Hanoi, Vietnam. Qualitative Research: Sixteen qualitative interviews revealed a complex variety of life experiences, beliefs and knowledge deficits that render these mostly poor and minimally educated men vulnerable to health problems including HIV infection. This study formed a conceptual model of numerous stressors related to migrants’ life experiences in urban space, including physical, financial and social factors. A wide range of coping strategies were adopted to deal with stressors – including problem-focused coping (PFC) and emotion-focused coping (EFC), pro-social and anti-social, active and passive. These men reported difficulty in coping with stressors because they had weak social networks and lacked support from formal systems. A second conceptual model emerged that highlighted equivalent influences of individual psychological factors, social integration, social barriers, and accessibility regarding drug use and sexual risk behavior. Psychological dimensions such as tedium, distress, fatalism and revenge, were important. There were strong effects of collective decision-making and fear of social isolation on shaping risk behaviors. These exploratory qualitative interviews helped to develop a culturally appropriate instrument for the quantitative survey and informed theoretical models of the factors that affect risk behaviors for HIV infection. Quantitative Research: The Information-Motivation-Behavioral Skills (IMB) model was adopted as the theoretical framework for a large-scale survey. It was modified to suit the contexts of these Vietnamese men. By doing a social mapping technique, 450 male street laborers were interviewed in Hanoi, Vietnam. The survey revealed that the risk of acquiring and transmitting HIV was high among these men. One in every 12 men reported homosexual or bisexual behavior. These men on average had 3 partners within the preceding year, and condom use was inconsistent. One third had had sex with commercial sex workers (CSW) and only 30% of them reported condom use; 17% used illicit drugs sometimes, with 66.7% of them frequently sharing injecting equipment with peers. Despite the risks, only 19.8% of men had been tested for HIV during the previous 12 months. These men have limited HIV knowledge and only moderate motivation and perceived behavioral skills for protective behavior. Although rural-to-urban migration was not associated with sexual risk behavior, three elements of the IMB model and depression associated with the process of mobility were significant determinants of sexual behavior. A modified model that incorporated IMB elements and psychosocial stress was found to be a better fit than the original IMB model alone in predicting protected sex behavior among the men. Men who were less psychologically and socially stressed, better informed and motivated for HIV prevention were more likely to demonstrate behavioral skills, and in turn were more likely to engage in safer sexual behavior. With regard to drug use, although the conventional model accounted for slightly less variance than the modified IMB model, data were of better fit for the conventional model. Multivariate analyses revealed that men who originated from urban areas, those who were homo- or bi-sexually identified and had better knowledge and skills for HIV prevention were more likely to access HIV testing, while men who had more sexual partners and those who did not use a condom for sex with CSW were least likely to take a test. The modified IMB model provided a better fit than the conventional model, as it explained a greater variance in HIV testing. Conclusions and Implications: This research helps to highlight a potential hidden HIV epidemic among street male, unskilled, unregistered laborers. This group has multiple vulnerabilities to HIV infection through both their partners and peers. However, most do not know their HIV status and have limited knowledge about preventing infection. This is the first application of a modified IMB model of risk behaviors for HIV such as drug use, condom use, and uptake of HIV testing to research with male street laborers in urban settings. The study demonstrated that while the extended IMB model had better fit than the conventional version in explaining the behaviors of safe sex and HIV testing, it was not so for drug use. The results provide interesting directions for future research and suggest ways to effectively design intervention strategies. The findings should shed light on culturally appropriate HIV preventive education and support programs for these men. As Vietnam has much in common with other developing countries in Southeast Asia, this research provides evidence for policy and practice that may be useful for public health systems in similar countries.

A hybrid model for studying spatial aspects of infectious diseases

We consider a hybrid model, created by coupling a continuum and an agent-based model of infectious disease. The framework of the hybrid model provides a mechanism to study the spread of infection at both the individual and population levels. This approach captures the stochastic spatial heterogeneity at the individual level, which is directly related to deterministic population level properties. This facilitates the study of spatial aspects of the epidemic process. A spatial analysis, involving counting the number of infectious agents in equally sized bins, reveals when the spatial domain is nonhomogeneous.

Treatment for prevention of HIV transmission in a localised epidemic : the case for South Australia

Background: Discussion is currently taking place among international HIV/AIDS groups around increasing HIV testing and initiating earlier use of antiretroviral therapy (ART) among people diagnosed with HIV as a method to reduce the spread of HIV. In this study, we explore the expected epidemiological impact of this strategy in a small population in which HIV transmission is predominantly confined to men who have sex with men (MSM). Methods: A deterministic mathematical transmission model was constructed to investigate the impacts of strategies that increase testing and treatment rates, and their likely potential to mitigate HIV epidemics among MSM. Our novel model distinguishes men in the population who are more easily accessible to prevention campaigns through engagement with the gay community from men who are not. This model is applied to the population of MSM in South Australia. Results: Our model-based findings suggest that increasing testing rates alone will have minimal impact on reducing the expected number of infections compared to current conditions. However, in combination with increases in treatment coverage, this strategy could lead to a 59–68% reduction in the number of HIV infections over the next 5 years. Targeting men who are socially engaged with the gay community would result in the majority of potential reductions in incidence, with only minor improvements possible by reaching all other MSM. Conclusions: Investing in strategies that will achieve higher coverage and earlier initiation of treatment to reduce infectiousness of HIV-infected individuals could be an effective strategy for reducing incidence in a population of MSM.

A parallel approach to social network generation and agent-based epidemic simulation

Understanding the dynamics of disease spread is essential in contexts such as estimating load on medical services, as well as risk assessment and interven- tion policies against large-scale epidemic outbreaks. However, most of the information is available after the outbreak itself, and preemptive assessment is far from trivial. Here, we report on an agent-based model developed to investigate such epidemic events in a stylised urban environment. For most diseases, infection of a new individual may occur from casual contact in crowds as well as from repeated interactions with social partners such as work colleagues or family members. Our model therefore accounts for these two phenomena. Given the scale of the system, efficient parallel computing is required. In this presentation, we focus on aspects related to paralllelisation for large networks generation and massively multi-agent simulations.