Disease-structured N-mixture models: A practical guide to model disease dynamics using count data.

Graziella V Direnzo,Christian Che‐Castaldo,Elise F Zipkin,Sarah P Saunders,Evan H Campbell Grant

doi:10.1002/ece3.4849

Graziella V Direnzo, Christian Che‐Castaldo + Show 3 more

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https://doi.org/10.1002/ece3.4849

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Abstract

Obtaining inferences on disease dynamics (e.g., host population size, pathogen prevalence, transmission rate, host survival probability) typically requires marking and tracking individuals over time. While multistate mark–recapture models can produce high‐quality inference, these techniques are difficult to employ at large spatial and long temporal scales or in small remnant host populations decimated by virulent pathogens, where low recapture rates may preclude the use of mark–recapture techniques. Recently developed N‐mixture models offer a statistical framework for estimating wildlife disease dynamics from count data. N‐mixture models are a type of state‐space model in which observation error is attributed to failing to detect some individuals when they are present (i.e., false negatives). The analysis approach uses repeated surveys of sites over a period of population closure to estimate detection probability. We review the challenges of modeling disease dynamics and describe how N‐mixture models can be used to estimate common metrics, including pathogen prevalence, transmission, and recovery rates while accounting for imperfect host and pathogen detection. We also offer a perspective on future research directions at the intersection of quantitative and disease ecology, including the estimation of false positives in pathogen presence, spatially explicit disease‐structured N‐mixture models, and the integration of other data types with count data to inform disease dynamics. Managers rely on accurate and precise estimates of disease dynamics to develop strategies to mitigate pathogen impacts on host populations. At a time when pathogens pose one of the greatest threats to biodiversity, statistical methods that lead to robust inferences on host populations are critically needed for rapid, rather than incremental, assessments of the impacts of emerging infectious diseases.

Highlights

Emerging infectious diseases threaten human health, food security, and global biodiversity (Daszak, Cunningham, & Hyatt, 2000; Fisher et al, 2012; Jones et al, 2008)
Advanced sta‐ tistical methods that provide similar inferences as mark–recapture models for unmarked host populations are critically needed to understand disease dynamics, assess pathogen impacts on pop‐ ulations, and develop pathogen mitigation strategies.We highlight the utility of N‐mixture models (Dail & Madsen, 2011; Hostetler & Chandler, 2015; Royle, 2004; Zipkin, Sillett, et al, 2014; Zipkin, Thorson, et al, 2014) to study disease dynamics using count data
We focus on N‐mixture models and their variants because they pro‐ vide demographic estimates and detailed disease dynamics (Table 1), whereas detection/non‐detection approaches only estimate

Summary

| INTRODUCTION

Emerging infectious diseases threaten human health, food security, and global biodiversity (Daszak, Cunningham, & Hyatt, 2000; Fisher et al, 2012; Jones et al, 2008). The parameters δ0, δ1, μi, and σ2 are estimable by either (a) collecting multiple (>1) samples for diagnostic analysis from each observed host or (b) repeated diagnostic runs for individual samples, to explicitly model the relationship between pathogen infection intensity and pathogen detection probability In cases where such data are unavailable, infor‐ mation obtained from outside studies can be used. In the multiseason formulation of the disease‐structured N‐mix‐ ture model, our goal is to estimate the number of individuals (e.g., infected, uninfected), demographic parameters (e.g., survival, re‐ cruitment rates), and disease dynamics (i.e., transmission, recovery probabilities; Figure 2). The observa‐ tion model linking the observed survey data (i.e., repeated counts of infected and uninfected hosts at sites) for the open population model is the same as in the closed population model with the only difference being that the data and true latent abundance of hosts in disease state s at each site j during primary season, Ns,i,t, are all indexed by season/year t. Developed approaches, such as integrated population models and integrated distribution models, combine different types of data including count, detection–non‐detection, mark–recapture data, or opportunistic presence only

| CONCLUSIONS

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