A Model of Vascular Tumor Response to Chemotherapy Combined with Anti-Angiogenic Therapy

Flora S. Bacelar... et al.Angiogenesis is acknowledged as an essential mechanism for tumor spreading and metastasis of neoplastic diseases. Consequently, anti-angiogenic therapy has been proposed as a complementary or perhaps an alternative strategy to the traditional cytotoxic therapies. This work considers a model of ordinary di®erential equations that describe the dynamics of tumors at the vascular stage (after the angiogenic process has been triggered), under the action of chemical and anti-angiogenic ther- apies. Due to the increase of endothelial cells at the vascular stage, the cancer state prevails over the internal state in the no treatment situation. Results from the lo- cal stability analysis and numerical integration, indicate that the combination of chemotherapy and anti-angiogenic therapy is the best strategy to eliminate the tu- mor, reducing the cytotoxic e®ect. At a ¯xed infusion rate, the cure state may be reached when the combined therapy is considered but not for the anti-angiogenic therapy only. On the other hand, pure chemotherapy efectively destroys the tumor, but only when higher infusion doses are applied.Acknowledgments: STRP, RFSA thank CNPq for partial supporting the re- searchPeer reviewe

Life history and mating systems select for male biased parasitism mediated through natural selection and ecological feedbacks

Males are often the "sicker" sex with male biased parasitism found in a taxonomically diverse range of species. There is considerable interest in the processes that could underlie the evolution of sex-biased parasitism. Mating system differences along with differences in lifespan may play a key role. We examine whether these factors are likely to lead to male-biased parasitism through natural selection taking into account the critical role that ecological feedbacks play in the evolution of defence. We use a host-parasite model with two-sexes and the techniques of adaptive dynamics to investigate how mating system and sexual differences in competitive ability and longevity can select for a bias in the rates of parasitism. Male-biased parasitism is selected for when males have a shorter average lifespan or when males are subject to greater competition for resources. Male-biased parasitism evolves as a consequence of sexual differences in life history that produce a greater proportion of susceptible females than males and therefore reduce the cost of avoiding parasitism in males. Different mating systems such as monogamy, polygamy or polyandry did not produce a bias in parasitism through these ecological feedbacks but may accentuate an existing bias.Comment: 18 pages, 4 figure

Joint effects of nutrients and contaminants on the dynamics of a food chain in marine ecosystems

We analyze the joint effect of contaminants and nutrient loading on population dynamics of marine food chains by means of bifurcation analysis. Contaminant toxicity is assumed to alter mortality of some species with a sigmoidal dose-response relationship. A generic effect of pollutants is to delay transitions to complex dynamical states towards higher nutrient load values, but more counterintuitive consequences arising from indirect effects are described. In particular, the top predator seems to be the species more affected by pollutants, even when contaminant is toxic only to lower trophic levels

Exploring the tug of war between positive and negative interactions among savanna trees: Competition, dispersal, and protection from fire

arXiv:1304.6623Savannas are characterized by a discontinuous tree layer superimposed on a continuous layer of grass. Identifying the mechanisms that facilitate this tree-grass coexistence has remained a persistent challenge in ecology and is known as the "savanna problem". In this work, we propose a model that combines a previous savanna model Calabrese et al., 2010, which includes competitive interactions among trees and dispersal, with the Drossel-Schwabl forest fire model, therefore representing fire in a spatially explicit manner. The model is used to explore how the pattern of fire-spread, coupled with an explicit, fire-vulnerable tree life stage, affects tree density and spatial pattern. Tree density depends strongly on both fire frequency and tree-tree competition although the fire frequency, which induces indirect interactions between trees and between trees and grass, appears to be the crucial factor controlling the tree-extinction transition in which the savanna becomes grassland. Depending on parameters, adult trees may arrange in different regular or clumped patterns, the later of two different types (compact or open). Cluster-size distributions have fat tails but clean power-law behavior is only attained in specific cases. © 2013 Elsevier B.V.F.S.B. and E.H.-G. acknowledge financial support from Spanish MINECO and FEDER through project FISICOS (FIS2007-60327). J.M.C acknowledges the support of the European Union project PATRES (Pattern Re-silience; project NEST 43268). F.S.B. acknowledges a grant from the Balearic Government.N

A model of partial differential equations for HIV propagation in lymph nodes

Texto completo versión postprint de autor.-- PACS numbers: 02.30.Ks,02.30.Hq,87.18.Hf,87.19.XxA system of partial differential equations is used to model the dissemination of the Human Immunodeficiency Virus (HIV) in CD4+T cells within lymph nodes. Besides diffusion terms, the model also includes a time-delay dependence to describe the time lag required by the immunologic system to provide defenses to new virus strains. The resulting dynamics strongly depends on the properties of the invariant sets of the model, consisting of three fixed points related to the time independent and spatial homogeneous tissue configurations in healthy and infected states. A region in the parameter space is considered, for which the time dependence of the space averaged model variables follows the clinical pattern reported for infected patients: a short scale primary infection, followed by a long latency period of almost complete recovery and third phase characterized by damped oscillations around a value with large HIV counting. Depending on the value of the diffusion coefficient, the latency time increases with respect to that one obtained for the space homogeneous version of the model. It is found that same initial conditions lead to quite different spatial patterns, which depend strongly on the latency interval.This work was partially supported by the following Brazilian funding agencies: CAPES, FAPESB/PRONEX, CNPq and National Institute for Science and Technology/Complex Systems.Peer reviewe

A mathematical model for the effect of anti-angiogenic therapy in the treatment of cancer tumours by chemotherapy

A model consisting of a system of five ordinary differential equations to simulate the interactions between normal cells, cancer cells, endothelial cells, chemotherapy agent and anti-angiogenic agent in tumour growth is developed. By a partial analysis of the cancer-free subspace, it is shown how the anti-angiogenic agent may help the chemotherapy agent in controlling the cancer. This is illustrated by numerical examples and bifurcation diagrams. © 2012 Published by Elsevier Ltd.This work has been partially supported by the Brazilian agencies CNPq (INCT—Complex Systems, INCT-CITECS), FAPESB/PRONEX, and the Spanish Agency AECI.Peer Reviewe

Synchronization unveils the organization of ecological networks with positive and negative interactions

International audienceNetwork science has helped to understand the organization principles of the interactions among the constituents of large complex systems. However, recently, the high resolution of the data sets collected has allowed to capture the different types of interactions coexisting within the same system. A particularly important example is that of systems with positive and negative interactions, a usual feature appearing in social, neural, and ecological systems. The interplay of links of opposite sign presents natural difficulties for generalizing typical concepts and tools applied to unsigned networks and, moreover, poses some questions intrinsic to the signed nature of the network, such as how are negative interactions balanced by positive ones so to allow the coexistence and survival of competitors/foes within the same system? Here, we show that synchronization phenomenon is an ideal benchmark for uncovering such balance and, as a byproduct, to assess which nodes play a critical role in the overall organization of the system. We illustrate our findings with the analysis of synthetic and real ecological networks in which facilitation and competitive interactions coexist