Global sensitivity analysis for stochastic models of infectious diseases: Re-emergence of yellow fever virus in the Americas as a case study

Abstract Emerging infectious diseases are a persistent public health threat that challenge deterministic, mechanistic modeling approaches. Because outbreaks initially start with a low number of infected hosts, their dynamics are highly stochastic, making traditional deterministic methods, e.g. ordinary differential equations, unable to qualitatively or quantitatively capture the transmission dynamics. In place, stochastic models are used, such as Markov chain models, but these models present their own challenges. Often, to infer a quantity of interest with stochastic models, we need to sample the model’s distribution many times over, introducing an additional source of noise to our analysis. This additional noise makes the inference of our quantity of interest more difficult and computationally expensive. Here, we show how novel tools from the field of uncertainty quantification can be used to efficiently separate these two channels of noise, allowing us to make rigorous statistical inferences about processes important for disease emergence. We illustrate these techniques with a model of yellow fever virus spillover in the Americas, a virus that has seen rapid re-emergence amongst multiple hosts and vectors in South America over the last decade. We show that only a handful of parameters’ uncertainties greatly affect variation in cumulative disease incidence. In particular, uncertainty in patch connectivity and non-human primate latency has the greatest impact on the variation of cumulative disease incidence of yellow fever virus across patches. Author Contributions Conceptualization: Nate Kornetzke, Helen J. Wearing. Methodology: Nate Kornetzke, Helen J. Wearing. Formal Analysis: Nate Kornetzke. Software: Nate Kornetzke. Visualization: Nate Kornetzke. Writing, Original Draft Preparation: Nate Kornetzke. Writing, Review and Editing: Helen J. Wearing. Supervision: Helen J. Wearing. Author Summary Emerging infectious diseases are a growing threat to public health. Computational models allow researchers to forecast future disease burdens and to investigate counterfactual scenarios, and often, these models are stochastic, i.e. contain randomness, to capture the qualitative behavior of emergence. A type of statistical analysis known as global sensitivity analysis allows modelers to rigorously analyze how varying the input to a model affects variation in its outputs. This type of analysis helps us infer what mechanisms are important for disease mitigation and control, especially when an infectious disease has a complex ecology consisting of multiple hosts and vectors. Until recently, stochastic models of emerging infectious diseases often proved too computationally expensive to perform a global sensitivity analysis on. Here, we demonstrate how new mathematical tools allow us to streamline this process for complex models of emerging infectious diseases. We analyze the ecology of re-emerging yellow fever in South America, a public health threat occurring in many hosts and vectors across vastly different ecosystems.