
Águas, R.; Lourenço, J.M.L.; Gomes, M.G.M.; White, L.J.
BACKGROUND: Clinical management of malaria is a major health issue in subSaharan Africa. New strategies based on intermittent preventive treatment (IPT) can tackle disease burden by simultaneously reducing frequency of infections and lifethreatening illness in infants (IPTi) and children (IPTc), while allowing for immunity to build up. However, concerns as to whether immunity develops efficiently in treated individuals, and whether there is a rebound effect after treatment is halted, have made it imperative to define the effects that IPTi and IPTc exert on the clinical malaria scenario. METHODS AND FINDINGS: Here, we simulate several schemes of intervention under different transmission...

Bacäer, N.; Gomes, M.G.M.
We first study an SIR system of differential equations with periodic coefficients describing an epidemic in a seasonal environment. Unlike in a constant environment, the final epidemic size may not be an increasing function of the basic reproduction number ℛ0 or of the initial fraction of infected people. Moreover, large epidemics can happen even if ℛ0<1. But like in a constant environment, the final epidemic size tends to 0 when ℛ0<1 and the initial fraction of infected people tends to 0. When ℛ0>1, the final epidemic size is bigger than the fraction 1−1/ℛ0 of the initially nonimmune population. In summary,...

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 susceptibleinfectedrecoveredinfected (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...

Gomes, M. G. M.; Medley, G. F.; Nokes, D. J.
Many pathogens exhibit antigenic diversity and elicit strainspecific immune responses. This potential for crossimmunity 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 patternforming 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 strainspace. Results are robust to strain number, but sensitive to the mechanism of cumulative immunity

Gomes, M. G. M.; Franco, A. O.; Gomes, M. C.; Medley, G. F.
Population patterns of infection are determined largely by susceptibility to infection. Infection and vaccination induce an immune response that, typically, reduces susceptibility to subsequent infections. With a general epidemic model, we detect a 'reinfection threshold', above which reinfection is the principal type of transmission and, consequently, infection levels are much higher and vaccination fails. The model is further developed to address human tuberculosis (TB) and the impact of vaccination. The bacille CalmetteGuérin (BCG) is the only vaccine in current use against TB, and there is no consensus about its usefulness. Estimates of protection range from 0 to 80%, and this...

Gomes, M. G. M.; White, L. J.; Medley, G. F.
The SIR (susceptibleinfectiousresistant) and SIS (susceptibleinfectioussusceptible) 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...

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 selfsustained 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 diseasefree equilibrium as transmission crosses this threshold. Consequently,...

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 (susceptibleinfectiousresistant) to the SIS (susceptibleinfectioussusceptible) 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 BogdanovTakens points are given

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 crossimmunity. Individual based simulations of this model on a 'smallworld' 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...

Gomes, Maria Gabriela Miranda; Águas, R.; Gonçalves, G.
Since the 1980s, the occurrence of pertussis cases in developed countries has increased and shifted towards older age groups. This resurgence follows 30 years of intense mass vaccination, and has been attributed primarily to three factors: (1) more effective diagnosis of the disease, (2) waning of vaccineinduced immunity, and (3) loss of vaccine efficacy due to the emergence of new Bordetella pertussis strains. Here we develop and analyse a mathematical model to assess the plausibility of these hypotheses. We consider that exposure to B pertussis through natural infection or vaccination induces an immune response that prevents severe disease but does...

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 antituberculosis drugs and those that are resistant. Our objective is to characterise the role of reinfection in the transmission of drugresistant tuberculosis. The longterm behaviour of our model reflects how reinfection modifies the conditions for coexistence of sensitive and resistant strains....

Gokaydin, D.; OliveiraMartins, J. B.; Gordo, I.; Gomes, M. G. M.
The awareness that pathogens can adapt and evolve over relatively short timescales is changing our view of infectious disease epidemiology and control. Research on the transmission dynamics of antigenically diverse pathogens is progressing and there is increasing recognition for the need of new concepts and theories. Mathematical models have been developed considering the modelling unit in two extreme scales: either diversity is not explicitly represented or diversity is represented at the finest scale of single variants. Here, we use an intermediate approach and construct a model at the scale of clusters of variants. The model captures essential properties of more...

Gomes, M. G. M.; Rodrigues, P.; Hilker, F. M.; MantillaBeniers, N. B.; Muehlen, M.; Paulo, A. C.; Medley, G. F.
Onethird 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 postexposure 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 postexposure vaccines can reduce the risk of reinfection. Here we develop mathematical models to explore the potential of these postexposure interventions to control tuberculosis...

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 onedimensional flowinvariant 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...

Parker, M. J.; Stewart, I. N.; Gomes, M. G. M.
Physical systems often exhibit patternforming 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 twelvedimensional representation of the hexagonal lattice where the symmetry of the model is perfect. Here, perturbation of group orbits of translationfree axial planforms in the six and twelvedimensional 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...

Aguas, R.; White, L. J.; Snow R.W.; Gomes M.G.M.
BACKGROUND: A characteristic of Plasmodium falciparum infections is the gradual acquisition of clinical immunity resulting from repeated exposures to the parasite. While the molecular basis of protection against clinical malaria remains unresolved, its effects on epidemiological patterns are well recognized. Accumulating epidemiological data constitute a valuable resource that must be intensively explored and interpreted as to effectively inform control planning. METHODOLOGY/PRINCIPAL FINDING: Here we apply a mathematical model to clinical data from eight endemic regions in subSaharan Africa. The model provides a quantitative framework within which differences in age distribution of clinical disease are assessed in terms of the parameters...

Paulo, A. C.; Gomes, M. C.; Gomes, M. G. M.
The alltime 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 cohortbycohort basis, and incorporate this information into an agestructured seasonallydriven mathematical model aimed at reproducing measles dynamics in the past decades. The model reproduces documented trends in disease notifications and the serological profile of...

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 susceptibleinfectedrecovered 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...