Nuno R. Martins

Optimal homotopy analysis of a chaotic HIV-1 model incorporating AIDS-related cancer cells

The studies of nonlinear models in epidemiology have generated a deep interest in gaining insight into the mechanisms that underlie AIDS-related cancers, providing us with a better understanding of cancer immunity and viral oncogenesis. In this article, we analyze an HIV-1 model incorporating the relations between three dynamical variables: cancer cells, healthy CD4 + T lymphocytes, and infected CD4 + T lymphocytes. Recent theoretical investigations indicate that these cells interactions lead to different dynamical outcomes, for instance to periodic or chaotic behavior. Firstly, we analytically prove the boundedness of the trajectories in the system’s attractor. The complexity of the coupling between the dynamical variables is quantified using observability indices. Our calculations reveal that the highest observable variable is the population of cancer cells, thus indicating that these cells could be monitored in future experiments in order to obtain time series for attractor’s reconstruction. We identify different dynamical behaviors of the system varying two biologically meaningful parameters: r1, representing the uncontrolled proliferation rate of cancer cells, and k1, denoting the immune system’s killing rate of cancer cells. The maximum Lyapunov exponent is computed to identify the chaotic regimes. Considering very recent developments in the literature related to the homotopy analysis method (HAM), we calculate the explicit series solutions of the cancer model and focus our analysis on the dynamical variable with the highest observability index. An optimal homotopy analysis approach is used to improve the computational efficiency of HAM by means of appropriate values for the convergence control parameter, which greatly accelerate the convergence of the series solution. The approximated analytical solutions are used to compute density plots, which allow us to discuss additional dynamical features of the model.

Green Architecture, Landscapes and Intercultural Dialogues

Urban Spaces in their interaction with cultural and artistic events produce differentiation, creating a dynamic encounter between the elites and the community as a whole (Shaw & Sullivan, 2011; Kallin, 2014) and offering a flourishing context for considering how culture is imminently connected with the effects on place making (Rota & Salone, 2014; Langegger, 2013). This reflection makes us reconsider adequate strategies in terms of local approaches to culture and the growing importance of ‘intangibilities‘ for the definition of the profile of a local community.