The reinfection threshold

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 reserve

Infection, reinfection, and vaccination under suboptimal immune protection: epidemiological perspectives

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 neede

Dynamical behaviour of epidemiological models with sub-optimal immunity and nonlinear incidence

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 give

The reinfection threshold promotes variability in tuberculosis epidemiology and vaccine efficacy

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 Calmette-Guérin (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 variability is aggravated by an association between low vaccine efficacy and high prevalence of the disease. We propose an explanation based on three postulates: (i) the potential for transmission varies between populations, owing to differences in socio-economic and environmental factors; (ii) exposure to mycobacteria induces an immune response that is partially protective against reinfection; and (iii) this protection is not significantly improved by BCG vaccination. These postulates combine to reproduce the observed trends, and this is attributed to a reinfection threshold intrinsic to the transmission dynamics. Finally, we demonstrate how reinfection thresholds can be manipulated by vaccination programmes, suggesting that they have a potentially powerful role in global contro

The development and validation of an age-structured model for the evaluation of disease control strategies for intestinal helminths

Epidemiological modelling can be a useful tool for the evaluation of parasite control strategies. An age-structured epidemiological model of intestinal helminth dynamics is developed. This model includes the explicit representation of changing worm distributions between hosts as a result of treatment, and estimates the morbidity due to heavy infections. The model is used to evaluate the effectiveness of different programmes of age-targeted community chemotherapy in reducing the amount of morbidity due to helminth infection. The magnitude of age-related heterogeneities is found to be very important in determining the results of age-targeted treatment programmes. The model was verified using field data from control programmes for Ascaris lumbricoides and Trichuris trichiura, and was found to provide accurate predictions of prevalence and mean intensities of infection during and following different control regime

Density-dependent processes in the transmission of human onchocerciasis: relationship between the numbers of microfilariae ingested and successful larval development in the simuliid vector

A previous paper reported that the intake of Onchocerca volvulus microfilariae (mff) by different species of Simulium is essentially proportional to the parasite load in the skin of infected carriers. This paper examines the fate of the ingested mff in susceptible vectors to assess the relationship between parasite intake and infective larval output in blackfly species with and without well-developed cibarial armatures. Analysis is based on data from 3 onchocerciasis endemic areas: Guatemala (S. ochraceum s.l.), West Africa (S. damnosum s.l./S. sirbanum) and the Amazonian focus between South Venezuela and Northern Brazil (S. guianense and S. oyapockense s.l.). The data, which include published and unedited information collected in the field, record experimental studies of parasite uptake by wild flies maintained in captivity until the completion of the extrinsic incubation period. The relationship between L3 output (measured as the mean number of successful larvae/fly or, as the proportion of flies with infective larvae) and average microfilarial intake, was strongly non-linear. This non-linearity was best represented by a sigmoid function in case of armed simuliids (S. ochraceum s.l., S. oyapockense s.l.), or by a hyperbolic expression in that of unarmed flies (S. damnosum s.l., S. guianense). These results are compatible, respectively, with the patterns of ‘initial facilitation' and ‘limitation' described in culicid vectors of lymphatic filariases. A maximum mean number of 1-3 L3/fly was observed in all 4 vectors. It is concluded that O. volvulus larval development to the infective stage is regulated by density-dependent mechanisms acting at the early phase of microfilarial migration out of the blackfly's bloodmeal. Damage by the bucco-pharyngeal armature may also be density dependent. A hypothesis, based on this density dependence is forwarded to explain initial facilitation, so far only recorded in vectors with well-developed cibarial teeth. Our results provide quantitative support for the conjecture that chemotherapy alone is likely to have a greater impact on reducing onchocerciasis transmission in endemic areas where the main vector has a toothed fore-gut than in foci where the vectors have unarmed cibari

Epidemiological patterns of hepatitis B virus (HBV) in highly endemic areas

This paper uses meta-analysis of published data and a deterministic mathematical model of hepatitis B virus (HBV) transmission to describe the patterns of HBV infection in high endemicity areas. We describe the association between the prevalence of carriers and a simple measure of the rate of infection, the age at which half the population have been infected (A50), and assess the contribution of horizontal and perinatal transmission to this association. We found that the two main hyper-endemic areas of sub-Saharan Africa and east Asia have similar prevalences of carriers and values of A50, and that there is a negative nonlinear relationship between A50 and the prevalence of carriers in high endemicity areas (Spearman's Rank, P = 0·0086). We quantified the risk of perinatal transmission and the age-dependent rate of infection to allow a comparison between the main hyper-endemic areas. East Asia was found to have higher prevalences of HBeAg positive mothers and a greater risk of perinatal transmission from HBeAg positive mothers than sub-Saharan Africa, though the differences were not statistically significant. However, the two areas have similar magnitudes and age-dependent rates of horizontal transmission. Results of a simple compartmental model suggest that similar rates of horizontal transmission are sufficient to generate the similar patterns between A50 and the prevalences of carriers. Interrupting horizontal transmission by mass immunization is expected to have a significant, nonlinear impact on the rate of acquisition of new carriers

The development of an age structured model for schistosomiasis transmission dynamics and control and its validation for Schistosoma mansoni

Mathematical models are potentially useful tools to aid in the design of control programmes for parasitic diseases. In this paper, a fully age structured epidemiological model of human schistosomiasis is developed and parameterized, and used to predict trends in infection prevalence, intensity and prevalence of heavy infections over age and time during several rounds of mass and age targeted treatment. The model is validated against data from a Schistosoma mansoni control programme in Keny

A missing dimension in measures of vaccination impacts

Immunological protection, acquired from either natural infection or vaccination, varies among hosts, reflecting underlying biological variation and affecting population-level protection. Owing to the nature of resistance mechanisms, distributions of susceptibility and protection entangle with pathogen dose in a way that can be decoupled by adequately representing the dose dimension. Any infectious processes must depend in some fashion on dose, and empirical evidence exists for an effect of exposure dose on the probability of transmission to mumps-vaccinated hosts [1], the case-fatality ratio of measles [2], and the probability of infection and, given infection, of symptoms in cholera [3]. Extreme distributions of vaccine protection have been termed leaky (partially protects all hosts) and all-or-nothing (totally protects a proportion of hosts) [4]. These distributions can be distinguished in vaccine field trials from the time dependence of infections [5]. Frailty mixing models have also been proposed to estimate the distribution of protection from time to event data [6], [7], although the results are not comparable across regions unless there is explicit control for baseline transmission [8]. Distributions of host susceptibility and acquired protection can be estimated from dose-response data generated under controlled experimental conditions [9]–[11] and natural settings [12], [13]. These distributions can guide research on mechanisms of protection, as well as enable model validity across the entire range of transmission intensities. We argue for a shift to a dose-dimension paradigm in infectious disease science and community health

An intensive, active surveillance reveals continuous invasion and high diversity of rhinovirus in households

We report on infection patterns in 5 households (78 participants) delineating the natural history of human rhinovirus (HRV). Nasopharyngeal collections were obtained every 3–4 days irrespective of symptoms, over a 6-month period, with molecular screening for HRV and typing by sequencing VP4/VP2 junction. Overall, 311/3468 (8.9%) collections were HRV positive: 256 were classified into 3 species: 104 (40.6%) HRV-A; 14 (5.5%) HRV-B, and 138 (53.9%) HRV-C. Twenty-six known HRV types (13 HRV-A, 3 HRV-B, and 10 HRV-C) were identified (A75, C1, and C35 being most frequent). We observed continuous invasion and temporal clustering of HRV types in households (range 5–13 over 6 months). Intrahousehold transmission was independent of clinical status but influenced by age. Most (89.0%) of HRV infection episodes were limited to <14 days. Individual repeat infections were frequent (range 1–7 over 6 months), decreasing with age, and almost invariably heterotypic, indicative of lasting type-specific immunity and low cross-type protection