Impact of vaccination on the spatial correlation and persistence of measles dynamics.

Abstract

The onset of measles vaccination in England and Wales in 1968 coincided with a marked drop in the temporal correlation of epidemic patterns between major cities. We analyze a variety of hypotheses for the mechanisms driving this change. Straightforward stochastic models suggest that the interaction between a lowered susceptible population (and hence increased demographic noise) and nonlinear dynamics is sufficient to cause the observed drop in correlation. The decorrelation of epidemics could potentially lessen the chance of global extinction and so inhibit attempts at measles eradication.The combination of practical importance and theoretical interest has made measles in urban populations one of the most studied epidemiological systems, but spatial and stochastic effects remain less well explored (1). Practically, the continuing failure of mass vaccination campaigns to eradicate measles in developed countries and the importance of measles mortality among children in developing countries has led to continuing interest. Theoretically, recent work showing that nonlinear dynamics can reduce the extinction rate of spatially subdivided populations (2, 3) may be testable with the body of theory and data gathered to evaluate the persistence of measles and other childhood infections under mass vaccination (4-7).The basic dynamics of measles epidemics have been extensively studied (8-13). Large measles epidemics exhaust a pool of susceptible children, who gain lifelong immunity after having the disease; the interepidemic period is determined by the severity of the epidemic and the length of time taken to build up the pool of susceptibles again from new births. The seasonal pattern of aggregation of children in schools is also important in determining the size and pattern of epidemics (14-16). Furthermore, seasonality strongly influences the recurrent epidemic behavior of measles, where there is strong evidence for nonlinear (and possibly chaotic) effects (17-23).In small isolated communities, large epidemics are often followed by extinction of disease as the chain of transmission breaks down (8,24,25). The critical community size (8,24,26), the threshold population size above which measles can persist through interepidemic troughs, may depend on the spatial structure and connectedness of the regional population. The persistence behavior of measles is of particular interest in connection within the eradication of a disease by mass vaccination. Most theoretical estimates focus on the invasibility threshold, the level of control at which a disease will not only go extinct but also be unable to reinvade the population (13). One can also locally eradicate infection simply by driving it below its persistence threshold, the point at which the disease is likely to go extinct during the troughs between epidemics (27). The persistence threshold is greater than the invasibility threshold and hence easier to reach, but eradication through local extinction is fragile; reintroduction of the disease sparks a new epidemic, which...

Understanding the persistence of measles: reconciling theory, simulation and observation

“…This led to the notion of the critical community size (CCS), which is defined as the smallest population size that does not exhibit disease extinctions. The CCS has been estimated for a variety of communities, including cities in England and Wales (Bartlett 1957), cities in the United States (Bartlett 1960;Bolker & Grenfell 1996) and isolated islands (Black 1966). Surprisingly, its value is remarkably consistent between datasets, lying between three and five hundred thousand.…”

“…Given the robust nature of the CCS and the associated pattern of fade-outs, many researchers have attempted to capture these features using stochastic event-driven models (Bartlett 1956;Grenfell 1992;Grenfell et al 1995;Bolker & Grenfell 1996;Ferguson et al 1997;Keeling 1997;Keeling & Grenfell 1997). However, the persistence of real-world systems is an emergent phenomenon and arises from the interaction between dynamics and stochasticity.…”

On spatially explicit models of cholera epidemics

“…Most of the epidemiological literature has focused on contact networks that are crucial for understanding the evolution of diseases that are directly transmitted from individual to individual or from social group to social group (Diekmann et al 1990;Keeling 1999;Barthelemy et al 2005;Keeling & Eames 2005;Aparicio & Pascual 2007;Colizza & Vespignani 2007). Also, a good deal of work has been done with metapopulation-like models in which the disease is transmitted from patch to patch (Bolker & Grenfell 1996;Brooks et al 2008). Spatial models can be mapped into suitably defined contact network models (e.g.…”

Implications of vaccination and waning immunity

“…From the early investigations of disease models by Kermack & McKendrick (1927), to large-scale simulation models of pandemics ( Ferguson et al 2006), compartmental approaches have been used-this type of model groups individuals into one of a finite number of classes depending on their history of infection. The compartmental susceptible, exposed, infectious and recovered (SEIR) model has been intensively developed to understand the observed dynamics of acute infections, such as measles; extensions to the basic formulation include stochasticity (Bartlett 1956;Bolker & Grenfell 1996;Keeling & Grenfell 1997Keeling et al 2001;Finkenstädt et al 2002;Grenfell et al 2002), temporal forcing (Keeling & Grenfell 1997;Keeling et al 2001;Finkenstädt et al 2002;Bauch & Earn 2003), age-structure (Bolker 1993;Keeling & Grenfell 1997;Mossong & Muller 2003;Huang & Rohani 2006) and spatial structure (Bolker & Grenfell 1996;Keeling & Grenfell 1997;Earn et al 1998Earn et al , 2000Grenfell et al 2001). Measles has been the subject of many studies for two fundamental reasons: the first is that measles is still a significant cause of mortality and morbidity (20 million cases and 345 thousand deaths worldwide per year; WHO 2007), despite the existence of an inexpensive vaccine; the second is that extensive and detailed case-report records exist for measles in many countries and these records show interesting temporal dynamics (Finkenstädt & Grenfell 2000;Finkenstädt et al 2002).…”