Browsing by Author "Gomes, M. G. M."
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- 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
- 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
- Infection, reinfection, and vaccination under suboptimal immune protection: epidemiological perspectivesPublication . Gomes, M. G. M.; White, L. J.; Medley, G. F.The SIR (susceptible-infectious-resistant) and SIS (susceptible-infectious-susceptible) frameworks for infectious disease have been extensively studied and successfully applied. They implicitly assume the upper and lower limits of the range of possibilities for host immune response. However, the majority of infections do not fall into either of these extreme categories. We combine two general avenues that straddle this range: temporary immune protection (immunity wanes over time since infection), and partial immune protection (immunity is not fully protective but reduces the risk of reinfection). We present a systematic analysis of the dynamics and equilibrium properties of these models in comparison to SIR and SIS, and analyse the outcome of vaccination programmes. We describe how the waning of immunity shortens inter-epidemic periods, and poses major difficulties to disease eradication. We identify a "reinfection threshold" in transmission when partial immunity is included. Below the reinfection threshold primary infection dominates, levels of infection are low, and vaccination is highly effective (approximately an SIR model). Above the reinfection threshold reinfection dominates, levels of infection are high, and vaccination fails to protect (approximately an SIS situation). This association between high prevalence of infection and vaccine failure emphasizes the problems of controlling recurrent infections in high-burden regions. However, vaccines that induce a better protection than natural infection have the potential to increase the reinfection threshold, and therefore constitute interventions with a surprisingly high capacity to reduce infection where reduction is most needed
- Localized contacts between hosts reduce pathogen diversityPublication . Nunes, A.; da Gama, M. M. T.; Gomes, M. G. M.We investigate the dynamics of a simple epidemiological model for the invasion by a pathogen strain of a population where another strain circulates. We assume that reinfection by the same strain is possible but occurs at a reduced rate due to acquired immunity. The rate of reinfection by a distinct strain is also reduced due to cross-immunity. Individual based simulations of this model on a 'small-world' network show that the proportion of local contacts in the host contact network structure significantly affects the outcome of such an invasion, and as a consequence will affect the patterns of pathogen evolution. In particular, hosts interacting through a 'small-world' network of contacts support lower prevalence of infection than well-mixed populations, and the region in parameter space for which an invading strain can become endemic and coexist with the circulating strain is smaller, reducing the potential to accommodate pathogen diversity. We discuss the underlying mechanisms for the reported effects, and we propose an effective mean-field model to account for the contact structure of the host population in 'small-world' networks
- On the determinants of population structure in antigenically diverse pathogensPublication . Gomes, M. G. M.; Medley, G. F.; Nokes, D. J.Many pathogens exhibit antigenic diversity and elicit strain-specific immune responses. This potential for cross-immunity structure in the host resource motivates the development of mathematical models, stressing competition for susceptible hosts in driving pathogen population dynamics and genetics. Here we establish that certain model formulations exhibit characteristics of prototype pattern-forming systems, with pathogen population structure emerging as three possible patterns: (i) incidence is steady and homogeneous; (ii) incidence is steady but heterogeneous; and (iii) incidence shows oscillatory dynamics, with travelling waves in strain-space. Results are robust to strain number, but sensitive to the mechanism of cumulative immunity
- Partial classification of heteroclinic behaviour associated with the perturbation of hexagonal planformsPublication . Parker, M. J.; Stewart, I. N.; Gomes, M. G. M.Physical systems often exhibit pattern-forming instabilities. Equivariant bifurcation theory is often used to investigate the existence and stability of spatially doubly periodic solutions with respect to the hexagonal lattice. Previous studies have focused on the six- and twelve-dimensional representation of the hexagonal lattice where the symmetry of the model is perfect. Here, perturbation of group orbits of translation-free axial planforms in the six- and twelve-dimensional representations is considered. This problem is studied via the abstract action of the symmetry group of the perturbation on the group orbit of the planform. A partial classification for the behaviour of the group orbits is obtained, showing the existence of homoclinic and heteroclinic cycles between equilibria
- The reinfection thresholdPublication . Gomes, M. G. M.; White, L. J.; Medley, G. F.Thresholds in transmission are responsible for critical changes in infectious disease epidemiology. The epidemic threshold indicates whether infection invades a totally susceptible population. The reinfection threshold indicates whether self-sustained transmission occurs in a population that has developed a degree of partial immunity to the pathogen (by previous infection or vaccination). In models that combine susceptible and partially immune individuals, the reinfection threshold is technically not a bifurcation of equilibria as correctly pointed out by Breban and Blower. However, we show that a branch of equilibria to a reinfection submodel bifurcates from the disease-free equilibrium as transmission crosses this threshold. Consequently, the full model indicates that levels of infection increase by two orders of magnitude and the effect of mass vaccination becomes negligible as transmission increases across the reinfection threshold. (c) 2005 Elsevier Ltd. All rights reserved