Heterogeneity in susceptibility to infection can explain high reinfection rates

Abstract

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)...

The size of epidemics in populations with heterogeneous susceptibility

“…Several authors have previously formulated and studied epidemiological models with heterogenous susceptibility, either in terms of a finite number of different susceptibility classes (Andersson and Britton 1998;Ball 1985;Bonzi et al 2010;Gart 1972;Hyman and Li 2005;Rodrigues et al 2009;Scalia-Tomba 1986) or as a continuous distribution of susceptibility (Coutinho et al 1999;Diekmann and Heesterbeek 2000;Dwyer et al 1997Dwyer et al , 2000Novozhilov 2008). Below, as we describe our results, we will mention some of the results obtained in these works, and their relations with the present investigation.…”

Examining the reservoir potential of animal species for $$\varvec{\textit{Leishmania infantum}}$$ Leishmania infantum infection

“…Second, not necessarily directly surveying these characteristics through entomologic investigations, but also one could examine genetic or molecular characteristics of Leishmania spp. For instance, one could implement phylogenetic analysis to accurately capture the route of transmission and evolution, thereby permitting us to track the inter-specific transmission in an explicit manner [18][19][20][21][22][23][24][36][37][38]. Such analysis could also shed light on our assumption of SIS model (e.g.…”

“…Such analysis could also shed light on our assumption of SIS model (e.g. if there is immune reaction through frequent re-infections and if there is an indication of evolution of the pathogen) and analysis of genetic data does not force us to adopt a stationary state assumption [18][19][20][21][22][23][24].…”

“…Such evidence helps us to assume that all individuals never die of the infection and acquire immunity, and thus, to adopt an susceptible-infectious-susceptible (SIS) model [18][19][20][21][22][23][24]. Let x i and y i be proportions susceptible and infectious of species i, respectively, we have…”

How host heterogeneity governs tuberculosis reinfection?

“…This is again owing to the way differential recruitment acts upon individuals at higher risk. For highly endemic regions, transmission intensity tends to homogenize the distributions of both susceptible and recovered individuals, making differential recruitment less pronounced [34]. Cape Town is the only study reporting the information required to estimate this ratio.…”