Complex Agent Networks explaining the HIV epidemic among homosexual men in Amsterdam

Simulating the evolution of the Human Immunodeficiency Virus (HIV) epidemic requires a detailed description of the population network, especially for small populations in which individuals can be represented in detail and accuracy. In this paper, we introduce the concept of a Complex Agent Network(CAN) to model the HIV epidemics by combining agent-based modelling and complex networks, in which agents represent individuals that have sexual interactions. The applicability of CANs is demonstrated by constructing and executing a detailed HIV epidemic model for men who have sex with men (MSM) in Amsterdam, including a distinction between steady and casual relationships. We focus on MSM contacts because they play an important role in HIV epidemics and have been tracked in Amsterdam for a long time. Our experiments show good correspondence between the historical data of the Amsterdam cohort and the simulation results.Comment: 21 pages, 4 figures, Mathematics and Computers in Simulation, added reference

Bayesian inference for indirectly observed stochastic processes, applications to epidemic modelling

Stochastic processes are mathematical objects that offer a probabilistic representation of how some quantities evolve in time. In this thesis we focus on estimating the trajectory and parameters of dynamical systems in cases where only indirect observations of the driving stochastic process are available. We have first explored means to use weekly recorded numbers of cases of Influenza to capture how the frequency and nature of contacts made with infected individuals evolved in time. The latter was modelled with diffusions and can be used to quantify the impact of varying drivers of epidemics as holidays, climate, or prevention interventions. Following this idea, we have estimated how the frequency of condom use has evolved during the intervention of the Gates Foundation against HIV in India. In this setting, the available estimates of the proportion of individuals infected with HIV were not only indirect but also very scarce observations, leading to specific difficulties. At last, we developed a methodology for fractional Brownian motions (fBM), here a fractional stochastic volatility model, indirectly observed through market prices. The intractability of the likelihood function, requiring augmentation of the parameter space with the diffusion path, is ubiquitous in this thesis. We aimed for inference methods robust to refinements in time discretisations, made necessary to enforce accuracy of Euler schemes. The particle Marginal Metropolis Hastings (PMMH) algorithm exhibits this mesh free property. We propose the use of fast approximate filters as a pre-exploration tool to estimate the shape of the target density, for a quicker and more robust adaptation phase of the asymptotically exact algorithm. The fBM problem could not be treated with the PMMH, which required an alternative methodology based on reparameterisation and advanced Hamiltonian Monte Carlo techniques on the diffusion pathspace, that would also be applicable in the Markovian setting

Unsafe Sex, AIDS, and Development

Much of Africa has been ravaged by the AIDS epidemic. There, heterosexual contact is the primary mode of transmission for the HIV virus. Even when access to condoms is good and their price low, a large fraction of young Africans continue to engage in unprotected sex. In this paper, we propose a simple two period rational model of sexual behavior that has the potential to explain why a large proportion of sexual activity in poor countries maybe unprotected. In the model economy, even when agents are perfectly cognizant of the risk involved in unsafe sexual activity, and fully internalize the effects of their own sexual behavior on their chance of catching the virus, they may rationally choose to engage in such risky behavior. Our results indicate that safe sexual practice is essentially a "normal good" and that development may be key to reducing HIV infectivity.AIDS; rational choice; sexual behavior; safe sex

VI Workshop on Computational Data Analysis and Numerical Methods: Book of Abstracts

The VI Workshop on Computational Data Analysis and Numerical Methods (WCDANM) is going to be held on June 27-29, 2019, in the Department of Mathematics of the University of Beira Interior (UBI), Covilhã, Portugal and it is a unique opportunity to disseminate scientific research related to the areas of Mathematics in general, with particular relevance to the areas of Computational Data Analysis and Numerical Methods in theoretical and/or practical field, using new techniques, giving especial emphasis to applications in Medicine, Biology, Biotechnology, Engineering, Industry, Environmental Sciences, Finance, Insurance, Management and Administration. The meeting will provide a forum for discussion and debate of ideas with interest to the scientific community in general. With this meeting new scientific collaborations among colleagues, namely new collaborations in Masters and PhD projects are expected. The event is open to the entire scientific community (with or without communication/poster)