# Christopher J. Fonnesbeck$${}^{1}$$, Katriona Shea$${}^{2,3}$$, Spencer Carran$${}^{3}$$, Jose Cassio de Moraes$${}^{4}$$, Christopher Gregory$${}^{5}$$, James L. Goodson$${}^{6}$$, and Matthew Ferrari$${}^{2,3}$$ $${}^{1}$$Department of Biostatistics, Vanderbilt University School of Medicine, Eleventh Floor, Suite 11000, 2525 West End Avenue, Nashville, TN, USA $${}^{2}$$Department of Biology and Intercollege Graduate Degree Program in Ecology, 208 Mueller Laboratory, The Pennsylvania State University, University Park, Pennsylvania, USA $${}^{3}$$Center for Infectious Disease Dynamics, Department of Biology, Eberly College of Science, The Pennsylvania State University, University Park, Pennsylvania, USA $${}^{4}$$Faculdade de Ciencias Medicas da Sanda Casa de Sao Paulo, Sao Paulo, Brazil $${}^{5}$$Arboviral Diseases Branch, Division of Vector-Borne Diseases, National Center for Enteric and Zoonotic Infectious Diseases, US Centers for Disease Control and Prevention, Fort Collins, Colorado, USA $${}^{6}$$Accelerated Disease Control and Vaccine Preventable Disease Surveillance Branch, Global Immunization Division, Center for Global Health, US Centers for Disease Control and Prevention, Atlanta, Georgia, USA Journal for submission: Journal of the Royal Society Interface Abstract Word Count: 193 (Limit: 200) Text Word Count: 6421 (Limit: 8000), note this is inclusive of references and figure legends Table count: 0 (Limit: NA) Figure count: 5 (Limit: NA) References: 40 (Limit: NA)

Abstract

Resurgent outbreaks of vaccine-preventable diseases that have previously been controlled or eliminated have been observed in many settings. Reactive vaccination campaigns may successfully control outbreaks but must necessarily be implemented in the face of considerable uncertainty. Real-time surveillance may provide critical information about at-risk population and optimal vaccination targets, but may itself be limited by the specificity of disease confirmation. We propose an integrated modeling approach that synthesizes historical demographic and vaccination data with real-time outbreak surveillance via a dynamic transmission model and an age-specific disease confirmation model. We apply this framework to data from the 1996-7 measles outbreak in São Paulo, Brazil. To simulate the information available to decision-makers, we truncated the surveillance data to what would have been available at 1 or 2 months prior to the realized interventions. We use the model, fitted to real-time observations, to evaluate the likelihood that candidate age-targeted interventions could control the outbreak. Using only data available prior to the interventions, we estimate that a significant excess of susceptible adults would prevent child-targeted campaigns from controlling the outbreak and that failing to account for age-specific confirmation rates would under-estimate the importance of adult targeted vaccination.

## Introduction

\label{introduction}

Resurgent outbreaks of vaccine-preventable diseases following long periods of relative absence are an increasingly common phenomenon (Hersh 1991, Cherry 2012, Celentano 2005, Shibeshi 2014). Several factors may contribute to the occurrence of such outbreaks. McLean and Anderson (McLean 1988) predicted that such outbreaks should be expected because of the “honeymoon” phenomenon following the introduction of vaccination, whereby post-vaccination cohorts no longer experience high rates of natural immunization to supplement population immunity following vaccination activities (Jansen 2003). Further, population-level vaccination rates may decline over time as immigration from areas of low immunity lead to a buildup of susceptible individuals, or the reduction in individual infection risk (Omer 2009) leads to apathy about vaccination within the population. Also, local stochastic extinction may result in temporary breakdown of local transmission, even though populations remain susceptible to subsequent outbreaks upon the reintroduction of infection (Ferrari 2008).

Increasingly, in the event of a measles outbreak, outbreak response immunization (ORI) is recommended as an intervention. The goals of these ORIs are two-fold: 1) to protect high risk groups (i.e. young children) and 2) to attenuate the current outbreak (Cairns 2011, Grais 2011). To achieve the former goal, ORI campaigns routinely target children 6-59 months of age (Cairns 2011). To achieve the latter goal, the campaign must reach some target level of immunization — i.e. a percentage reduction of the susceptible population — such that effective reproductive number, $$R_{e}$$, will be below 1 and the outbreak will end. From the standard susceptible-infected-removed (SIR) model, this level of immunization is $$P_{c}=1-1/R_{e}$$ (Anderson 1981). To identify this target coverage and appropriately plan a campaign, one must estimate both the value of $$R_{e}$$ itself and the age distribution of the susceptible population, which determines the necessary reduction of the susceptible population required to end the outbreak and the critical age classes to be targeted in a campaign, respectively. For example, if $$R_{e}=1.5$$ one must then reduce the susceptible fraction by 33%; if 80% immunization of susceptibles in the target age groups can be achieved, then at a minimum, the intervention should target individuals up to the 100*(0.33/0.8) = 41.25th age percentile of the susceptible population.

Experience with past outbreaks can provide guidance about likely values of $$R_{e}$$ (Durrheim 2014) and the likely distribution of the susceptible population (Goodson 2011, Takahashi 2014). However, in the case of resurgent outbreaks, which follow periods of relatively low measles incidence, there may be insufficient data on which to base estimates of $$R_{e}$$. In these settings, it is the current outbreak itself which may provide the most relevant empirical information (Durrheim 2014, Merl 2009, Shea 2014). However, clinical confirmation of measles cases through case-based surveillance systems has relatively low specificity, particularly in settings of low prevalence (Hutchins 2004, Ho 2014, GUY 2004, Dietz 2004) when other illnesses that result in fever and rash (e.g. rubella, Dengue) may be misdiagnosed as measles (Ho 2014). Given that the various sources of febrile illness may disproportionately affect different age classes, reliance on a clinical definition alone may result in a biased assessment of the age classes at risk (Hutchins 2004, Durrheim 2014). Further, misdiagnosis of cases may bias the assessment of the rate of increase of total cases and lead to a biased estimate of $$R_{e}$$ and hence the vaccination coverage necessary to limit the outbreak. Though serological confirmation of measles cases is preferred to clinical confirmation, resources often limit the proportion of clinical cases that can be confirmed by serology in outbreak settings.

A variety of methods are available to estimate $$R_{e}$$ from early surveillance data (Durrheim 2014, Chiew 2013, Ferrari 2005, Lipsitch 2003). The use of mathematical modeling to estimate the age distribution of the susceptible population during an outbreak is rare; decisions about age targeting have been classically based on prior experience or early evaluation of previously confirmed cases (Minetti 2013). Here we present an epidemic model that uses serological confirmation on a subset of cases to estimate age-specific confirmation, and use th