Collective Dynamics
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Collective dynamics is an integrating component of natural systems, fundamental to all sciences, from physics to biology and sociology. We seek any unifying principles underlying the forms of self-organization in large populations of interacting elements. Our approach combines mathematical and experimental systems.
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- Association between Recruitment Methods and Attrition in Internet-Based StudiesPublication . Bajardi, Paolo; Paolotti, Daniela; Vespignani, Alessandro; Eames, Ken; Funk, Sebastian; Edmunds, W. John; Turbelin, Clement; Debin, Marion; Colizza, Vittoria; Smallenburg, Ronald; Koppeschaar, Carl; Franco, Ana O.; Faustino, Vitor; Carnahan, AnnaSara; Rehn, Moa; Merletti, Franco; Douwes, Jeroen; Firestone, Ridvan; Richiardi, LorenzoInternet-based systems for epidemiological studies have advantages over traditional approaches as they can potentially recruit and monitor a wider range of individuals in a relatively inexpensive fashion. We studied the association between communication strategies used for recruitment (offline, online, face-to-face) and follow-up participation in nine Internet-based cohorts: the Influenzanet network of platforms for influenza surveillance which includes seven cohorts in seven different European countries, the Italian birth cohort Ninfea and the New Zealand birth cohort ELF. Follow-up participation varied from 43% to 89% depending on the cohort. Although there were heterogeneities among studies, participants who became aware of the study through an online communication campaign compared with those through traditional offline media seemed to have a lower follow-up participation in 8 out of 9 cohorts. There were no clear differences in participation between participants enrolled face-to-face and those enrolled through other offline strategies. An Internet-based campaign for Internet-based epidemiological studies seems to be less effective than an offline one in enrolling volunteers who keep participating in follow-up questionnaires. This suggests that even for Internet-based epidemiological studies an offline enrollment campaign would be helpful in order to achieve a higher participation proportion and limit the cohort attrition.
- Comparative analysis of Streptococcus pneumoniae transmission in Portuguese and Finnish day-care centresPublication . Pessoa, Delphine; Hoti, Fabian; Syrjänen, Ritva; Sá-Leão, Raquel; Kaijalainen, Tarja; Gomes, M Gabriela M; Auranen, KariDay-care centre (DCC) attendees play a central role in maintaining the circulation of Streptococcus pneumoniae (pneumococcus) in the population. The prevalence of pneumococcal carriage is highest in DCC attendees but varies across countries and is found to be consistently lower in Finland than in Portugal. We compared key parameters underlying pneumococcal transmission in DCCs to understand which of these contributed to the observed differences in carriage prevalence.
- Controlling malaria using livestock-based interventions: a one health approachPublication . Franco, Ana O; Gomes, M Gabriela M; Rowland, Mark; Coleman, Paul G; Davies, Clive RWhere malaria is transmitted by zoophilic vectors, two types of malaria control strategies have been proposed based on animals: using livestock to divert vector biting from people (zooprophylaxis) or as baits to attract vectors to insecticide sources (insecticide-treated livestock). Opposing findings have been obtained on malaria zooprophylaxis, and despite the success of an insecticide-treated livestock trial in Pakistan, where malaria vectors are highly zoophilic, its effectiveness is yet to be formally tested in Africa where vectors are more anthropophilic. This study aims to clarify the different effects of livestock on malaria and to understand under what circumstances livestock-based interventions could play a role in malaria control programmes. This was explored by developing a mathematical model and combining it with data from Pakistan and Ethiopia. Consistent with previous work, a zooprophylactic effect of untreated livestock is predicted in two situations: if vector population density does not increase with livestock introduction, or if livestock numbers and availability to vectors are sufficiently high such that the increase in vector density is counteracted by the diversion of bites from humans to animals. Although, as expected, insecticide-treatment of livestock is predicted to be more beneficial in settings with highly zoophilic vectors, like South Asia, we find that the intervention could also considerably decrease malaria transmission in regions with more anthropophilic vectors, like Anopheles arabiensis in Africa, under specific circumstances: high treatment coverage of the livestock population, using a product with stronger or longer lasting insecticidal effect than in the Pakistan trial, and with small (ideally null) repellency effect, or if increasing the attractiveness of treated livestock to malaria vectors. The results suggest these are the most appropriate conditions for field testing insecticide-treated livestock in an Africa region with moderately zoophilic vectors, where this intervention could contribute to the integrated control of malaria and livestock diseases.
- Drug resistance in tuberculosis - a reinfection modelPublication . Rodrigues, P.; Gomes, M. G. M.; Rebelo, C.There is increasing recognition that reinfection is an important component of TB transmission. Moreover, it has been shown that partial immunity has significant epidemiological consequences, particularly in what concerns disease prevalence and effectiveness of control measures. We address the problem of drug resistance as a competition between two types of strains of Mycobacterium tuberculosis: those that are sensitive to anti-tuberculosis drugs and those that are resistant. Our objective is to characterise the role of reinfection in the transmission of drug-resistant tuberculosis. The long-term behaviour of our model reflects how reinfection modifies the conditions for coexistence of sensitive and resistant strains. This sets the scene for discussing how strain prevalence is affected by different control strategies. It is shown that intervention effectiveness is highly sensitive to the baseline epidemiological setting.
- Dynamical behaviour of epidemiological models with sub-optimal immunity and nonlinear incidencePublication . Gomes, M. G. M.; Margheri, A.; Medley, G. F.; Rebelo, C.In this paper we analyze the dynamics of two families of epidemiological models which correspond to transitions from the SIR (susceptible-infectious-resistant) to the SIS (susceptible-infectious-susceptible) frameworks. In these models we assume that the force of infection is a nonlinear function of density of infectious individuals, I. Conditions for the existence of backwards bifurcations, oscillations and Bogdanov-Takens points are given
- Dynamics and control of measles in Portugal: Accessing the impact of anticipating the age for the first dose of MMR from 15 to 12 months of agePublication . Paulo, A. C.; Gomes, M. C.; Gomes, M. G. M.The all-time low incidence of measles in Portugal in the recent years, raises questions regarding whether the disease has been eliminated, the role of recent control measures, and the epidemiological consequences of the rise in the proportion of newborns to vaccinated mothers, as opposed to those born to mothers who acquired immunity by natural infection. We estimate the vaccination coverage against measles in Portugal. on a cohort-by-cohort basis, and incorporate this information into an age-structured seasonally-driven mathematical model aimed at reproducing measles dynamics in the past decades. The model reproduces documented trends in disease notifications and the serological profile of the Portuguese population, as estimated by a recent National Serological, Survey. We provide evidence that the effective reproduction number (R-e) of measles has been driven below 1 in Portugal, and that sustained measles elimination is crucially dependent upon the maintenance of a high (>95%) coverage with the MMR I vaccine in the future. If the vaccination coverage decreases to levels around 90% the anticipation of the first dose of the MMR I from 15 to 12 months of age, will. ensure that R-e remains below 1. (C) 2008 Elsevier Ltd. All. rights reserved
- Examples of forced symmetry-breaking to homoclinic cycles in three-dimensional Euclidean-invariant systemsPublication . Parker, M. J.; Stewart, I. N.; Gomes, M. G. M.We study perturbations of cubic planforms, proving there exists perturbations with homoclinic cycles between persistent steady states. Our results do not depend on the representation of the symmetry group of the lattice, and are thus quite general. . The problem is studied using group theory rather than direct methods. We use the abstract action of the symmetry group of the perturbation on the group orbit to determine the existence of zero- and one-dimensional flow-invariant subspaces. The residual symmetry of the perturbation constrains the flows on these subspaces and, in certain cases, homoclinic cycles are guaranteed to exist. Cubic planforms are physically interesting due to their relevance to certain physical systems. Applications to reaction-diffusion systems, nonlinear optical systems and the polyacrylamide methylene blue oxygen reaction are discussed
- Genetic diversity in the SIR model of pathogen evolutionPublication . Gordo, I.; Gomes, M.G.M.; Reis, D.G.; Campos, P.R.A.We introduce a model for assessing the levels and patterns of genetic diversity in pathogen populations, whose epidemiology follows a susceptible-infected-recovered model (SIR). We model the population of pathogens as a metapopulation composed of subpopulations (infected hosts), where pathogens replicate and mutate. Hosts transmit pathogens to uninfected hosts. We show that the level of pathogen variation is well predicted by analytical expressions, such that pathogen neutral molecular variation is bounded by the level of infection and increases with the duration of infection. We then introduce selection in the model and study the invasion probability of a new pathogenic strain whose fitness (R0(1+s)) is higher than the fitness of the resident strain (R0). We show that this invasion probability is given by the relative increment in R0 of the new pathogen (s). By analyzing the patterns of genetic diversity in this framework, we identify the molecular signatures during the replacement and compare these with those observed in sequences of influenza A.
- Heterogeneity in susceptibility to infection can explain high reinfection ratesPublication . Rodrigues, P.; Margheri, A.; Rebelo, C.; Gomes, M.G.M.Heterogeneity in susceptibility and infectivity is inherent to infectious disease transmission in nature. Here we are concerned with the formulation of mathematical models that capture the essence of heterogeneity while keeping a simple structure suitable of analytical treatment. We explore the consequences of host heterogeneity in the susceptibility to infection for epidemiological models for which immunity conferred by infection is partially protective, known as susceptible-infected-recovered-infected (SIRI) models. We analyze the impact of heterogeneity on disease prevalence and contrast the susceptibility profiles of the subpopulations at risk for primary infection and reinfection. We present a systematic study in the case of two frailty groups. We predict that the average rate of reinfection may be higher than the average rate of primary infection, which may seem paradoxical given that primary infection induces life-long partial protection. Infection generates a selection mechanism whereby fit individuals remain in S and frail individuals are transferred to R. If this effect is strong enough we have a scenario where, on average, the rate of reinfection is higher than the rate of primary infection even though each individual has a risk reduction following primary infection. This mechanism may explain high rates of tuberculosis reinfection recently reported. Finally, the enhanced benefits of vaccination strategies that target the high-risk groups are quantified.
- Implications of partial immunity on the prospects for tuberculosis control by post-exposure interventionsPublication . Gomes, M. G. M.; Rodrigues, P.; Hilker, F. M.; Mantilla-Beniers, N. B.; Muehlen, M.; Paulo, A. C.; Medley, G. F.One-third of the world population (approximately 2 billion individuals) is currently infected with Mycobacterium tuberculosis, the vast majority harboring a latent infection. As the risk of reactivation is around 10% in a lifetime, it follows that 200 million of these will eventually develop active pulmonary disease. Only therapeutic or post-exposure interventions can tame this vast reservoir of infection. Treatment of latent infections can reduce the risk of reactivation, and there is accumulating evidence that combination with post-exposure vaccines can reduce the risk of reinfection. Here we develop mathematical models to explore the potential of these post-exposure interventions to control tuberculosis on a global scale. Intensive programs targeting recent infections appear generally effective, but the benefit is potentially greater in intermediate prevalence scenarios. Extending these strategies to longer-term persistent infections appears more beneficial where prevalence is low. Finally, we consider that susceptibility to reinfection is altered by therapy, and explore its epidemiological consequences. When we assume that therapy reduces susceptibility to subsequent reinfection, catastrophic dynamics are observed. Thus, a bipolar outcome is obtained, where either small or large reductions in prevalence levels result, depending on the rate of detection and treatment of latent infections. By contrast, increased susceptibility after therapy may induce an increase in disease prevalence and does not lead to catastrophic dynamics. These potential outcomes are silent unless a widespread intervention is implemented
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