The reinfection threshold

Gomes, M. Gabriela M.; White, Lisa J.; Medley, Graham F.

doi:10.1016/j.jtbi.2005.03.001

Cited by 65 publications

(40 citation statements)

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“…In both cases, disease persistence is determined by the threshold condition, R 0 41, irrespective of population structure, sustaining levels of infection that are generally much higher in the SIS scenario due to reinfection. In the intermediate case, another threshold has been identified, R 0 ¼ 1=s (Gomes et al, 2004(Gomes et al, , 2005, to describe a transition from SIRto SIS-like behavior. In Appendix C we show that the same expression holds for the reinfection threshold in the presence of heterogeneity in susceptibility to infection.…”

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Heterogeneity in susceptibility to infection can explain high reinfection rates

Rodrigues

Margheri

Rebelo

et al. 2009

Journal of Theoretical Biology

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parameters describing heterogeneity. Second, the same framework is used to explore the SIRI model. Of particular interest is the interplay between reinfection and the risk profile for the uninfected compartments, S and R. The results offer a plausible explanation for observations of higher than expected reinfection rates. In particular, rates of reinfection that surpass rates of first infection have been reported for tuberculosis in a high transmission setting in South Africa (Verver et al., 2005). Naively, one could attribute this effect to some form of immunologically dependent enhancement whereby immunological memory would render individuals more susceptible to subsequent infections. An alternative hypothesis suggested by the analysis presented here is that relatively high rates of reinfection can result from the presence of a high-risk group that, being at higher frequency in the recovered compartment due to selection imposed by the first infection, can sustain rates of reinfection that are, on average, higher than the rates of first infection even in the presence of partially protective immunity.Heterogeneity has many implications for public health policy. In particular, we characterise how the impact of vaccination strategies varies with transmission intensity, and quantify the benefit of targeting high-risk groups. The modelTo incorporate heterogeneity in the infection risk in an SIRI transmission model we use a formulation close to the one presented by Ball (1985) for SIR epidemic models. We assume that the population is divided in n different subgroups according to the susceptibility to infection, a i . These groups will be referred as frailty groups (Coutinho et al., 1999). Within each frailty group, individuals are classified according to their disease history into susceptible, infectious or recovered. A schematic version of the model is shown in Fig. 1.It is assumed that the n frailty groups have constant size over time and that they represent different proportions of the total population, g i , where P n i¼1 g i ¼ 1. Individuals are born into each group at the rate mg i . We use S i , I i and R i as the proportion of each class from the frailty group i in the total population. Hence we have P n i¼1 ðS i þ I i þ R i Þ ¼ 1. In the following we denote by I the proportion of infectious in the population, that is I ¼ P n i¼1 I i . For concreteness, we fix the parameters as described in Table 1. The table describes an average life expectancy of 70 years (that is m ¼ 1=70) and an average infectious period of one week (that is t ¼ 52). The factor reducing the risk of infection as a result of acquired immunity is s ¼ 0:25. For the limiting cases of the SIR and SIS models, parameter s is 0 or 1, respectively. Parameters b, g i and a i are varied to explore different scenarios for transmission intensity and host heterogeneity. Each frailty group has an average risk of infection that differs from the population average by a factor a i , which we refer to as the relative risk of infection (Gart, 1968;Ball, 1985)...

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Heterogeneity in susceptibility to infection can explain high reinfection rates

Rodrigues

Margheri

Rebelo

et al. 2009

Journal of Theoretical Biology

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“…If the cause of the resurgence is vaccine leakiness, then no worthwhile booster strategies are able to combat this problem (53), pointing toward the need for new vaccines (54). Our findings also emphasize the need for trouble-shooting pertussis resurgence; misdiagnosis of the problem will lead to implementing economically costly control measures with little or no epidemiological gains.…”

Section: Discussionmentioning

confidence: 81%

Combating pertussis resurgence: One booster vaccination schedule does not fit all

Riolo

Rohani

2015

Proc. Natl. Acad. Sci. U.S.A.

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Pertussis has reemerged as a major public health concern in many countries where it was once considered well controlled. Although the mechanisms responsible for continued pertussis circulation and resurgence remain elusive and contentious, many countries have nevertheless recommended booster vaccinations, the timing and number of which vary widely. Here, using a stochastic, age-stratified transmission model, we searched for cost-effective booster vaccination strategies using a genetic algorithm. We did so assuming four hypothesized mechanisms underpinning contemporary pertussis epidemiology: (I) insufficient coverage, (II) frequent primary vaccine failure, (III) waning of vaccine-derived protection, and (IV) vaccine "leakiness." For scenarios I-IV, successful booster strategies were identified and varied considerably by mechanism. Especially notable is the inability of booster schedules to alleviate resurgence when vaccines are leaky. Critically, our findings argue that the ultimate effectiveness of vaccine booster schedules will likely depend on correctly pinpointing the causes of resurgence, with misdiagnosis of the problem epidemiologically ineffective and economically costly.R econciling the historical successes of routine infant pertussis vaccination programs in reducing incidence (1-3) with the recent resurgence in a number of highly vaccinated countries (4, 5) has proved challenging, especially in the context of the global heterogeneity in contemporary pertussis epidemiology (6). A variety of explanations for pertussis resurgence have been proposed, ranging from improvements in surveillance and diagnostics (7) to reduced protection afforded by vaccination, whether due to the waning of vaccine-derived immunity (8), the evolution of the etiological agent (the bacterium Bordetella pertussis) (9), the switch from whole-cell to acellular vaccines (10), or the invasion and spread of Bordetella congeners (11). It has also been demonstrated that even in the absence of changes in the nature of transmission, vaccine, or reporting, pertussis resurgence might be expected in some countries as an inevitable consequence of insufficient historical vaccination (12).Disentangling the many pathways to pertussis resurgence is particularly difficult because pertussis immunity and, in particular, vaccine-derived immunity are not well understood (13). With no known reliable serological marker of protection (14), the properties of infection-and vaccine-derived immunity against pertussis must be inferred indirectly (15). However, the models of pertussis immunity that best reconcile individual-level clinical data (16) and population-level incidence data (17), respectively, are strikingly different. Data from serological studies (16, 18) and animal models (19) paint a picture of a vaccine that protects against disease for a limited duration and may afford little protection against transmission. In contrast, large-scale pertussis incidence data from countries such as Denmark (20), England and Wales (21), Thailand (17), and Sweden (2...

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“…This phenomenon can be understood in terms of the concept of reinfection threshold, 32 created for traditional compartmental systems with no mutation and reinfection. Systems with reinfection interpolate between SIR and SIS dynamics and, as the reinfection probability s increases, the equilibrium prevalence value changes from the SIR value to the much higher SIS value.…”

Section: Resultsmentioning

confidence: 99%

Host immunity and pathogen diversity: A computational study

Aquino

Nunes

2016

Virulence

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The distinctive features of human influenza A phylogeny have inspired many mathematical and computational studies of viral infections spreading in a host population, but our understanding of the mechanisms that shape the coupled evolution of host immunity, disease incidence and viral antigenic properties is far from complete. In this paper we explore the epidemiology and the phylogeny of a rapidly mutating pathogen in a host population with a weak immune response, that allows re-infection by the same strain and provides little cross-immunity. We find that mutation generates explosive diversity and that, as diversity grows, the system is driven to a very high prevalence level. This is in stark contrast with the behavior of similar models where mutation gives rise to a large epidemic followed by disease extinction, under the assumption that infection with a strain provides lifelong immunity. For low mutation rates, the behavior of the system shows the main qualitative features of influenza evolution. Our results highlight the importance of heterogeneity in the human immune response for understanding influenza A phenomenology. They are meant as a first step toward computationally affordable, individual based models including more complex host-pathogen interactions.

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The reinfection threshold

Cited by 65 publications

References 5 publications

Heterogeneity in susceptibility to infection can explain high reinfection rates

Heterogeneity in susceptibility to infection can explain high reinfection rates

Combating pertussis resurgence: One booster vaccination schedule does not fit all

Host immunity and pathogen diversity: A computational study

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