Ecological interventions to prevent and manage zoonotic pathogen spillover

Spillover of a pathogen from a wildlife reservoir into a human or livestock host requires the pathogen to overcome a hierarchical series of barriers. Interventions aimed at one or more of these barriers may be able to prevent the occurrence of spillover. Here, we demonstrate how interventions that target the ecological context in which spillover occurs (i.e. ecological interventions) can complement conventional approaches like vaccination, treatment, disinfection and chemical control. Accelerating spillover owing to environmental change requires effective, affordable, durable and scalable solutions that fully harness the complex processes involved in cross-species pathogen spillover. This article is part of the theme issue ‘Dynamic and integrative approaches to understanding pathogen spillover’.


Modelling methods
We defined a simple 2-host system, i.e., donors and recipients, with three compartmental classes, Susceptible-Infected-Recovered (SIR), for each host species, and spillover from donors to recipients [1]. Model simulations are conducted using an Euler-multinomial approximation to the two-host ordinary differential equation model. Our model builds off previously proposed frameworks (e.g. [2,3]), but our focus is more on the practical implications of potential interventions. Using a tractable framework, we focus on the comparative outcomes of simulated management options applied to either donor or recipient populations and highlight potential non-linearities in spillover risk that result. We use the model to simulate disease dynamics for two sets of fixed parameter values (Table 1). We examine how each particular ecological intervention applied to a single parameter (process) affects disease outcomes in recipient populations in terms of: 1) the total number of cases in the recipient population, and 2) the total number of spillover events in a defined timeframe.
Interventions were implemented as a fixed proportional reduction in a parameter value, except culling and vaccination, which were specified as annual proportions that were then converted to rates. We assumed that each specified intervention affected a single parameter.
Each simulation was run for 5 years using daily time steps with initial population sizes of 10000 hosts in each of the donor and recipient populations. We initialized all simulations at the endemic equilibrium (with values rounded) for the donor and at the disease-free equilibrium for the recipeint. We used parameter values representing two different example spillover systems, which differed in their assumed contact rates and durations of infection. We ran 1000 replicate simulations per ecological intervention condition. We present the average outcomes (total cases in the recipient population and total number of spillover events) in Figures S3-S6.
Model specification and assumptions are described below. Note that the modeling framework is intentionally simplistic because our goal is to visualize potential non-linearities in effects of different ecological interventions. This type of framework could be adapted to address ecological complexities of particular systems (e.g., environmental transmission, spatial structure, etc.). Currently, the framework is intended to generate hypotheses for further examination. file:///Users/pulliam/Dropbox%20(Personal)/Manuscripts/Published/LeversSpillover/PROOFS/rstb20180342/rstb20180342_si_001.webarchive Only spillover from donor to recipient, no spillback from recipient to donor Homogenous mixing in each population and between them Direct contact transmission only Lifelong immunity from infection or vaccination No disease-induced mortality All newborns are susceptible No spatial structure Density-dependent transmission; no other density-dependent processes Occaisional re-introduction of the pathogen into the donor host to prevent extinction (as would be expected if the pathogen were maintained in a donor host via metapopulation dynamics)

Model structure
We first specify the ordinary differential equation (ODE) model, based on the classic SIR compartmental framework (e.g., Keeling and Rohani 2007). We then implement a stochastic, discrete time approximation to the ODE system using an Euler-multinomial approach. Disease dynamics in the donor host ( ) are described by the following equations: and in the recipient host ( ): where all parameters are defined as in Table S1. For simulations wtih vaccination ( or ), the vaccination hazards (daily rates) are calculated from average fraction of hosts in the population vaccinated every year as , where . For simulations wtih culling ( ), the excess mortality hazard (daily rate) is similarly calculated from the annual fraction culled.
For this system, we can derive reproduction ratios for sub-component models (assuming no vaccination, i.e., ), namely: Rearranging these equations allows the calculation of a transmission coefficient from the associated reproduction ratio: .
Initial conditions are set based on the endemic equilibrium of the deterministic model (in the absence of interventions) for the donor and the disease free equilibrium for the recipient: These values are rounded to the nearest integer for initiation of the Euler-multinomial approximation. Figure S1: Structure of the two-host compartmental model used to explore the effects of ecological interventions. Solid arrows show rates of flow into and out of model compartments. Dashed arrows indicate influences that affect these rates. Table S1 shows all parameter definitions, including both model notation and variable names used in the code for model implementation. Baseline parameter values are given for two example pathogens. Example 1 represents a pathogen that has supercritical transmission in the recipient host ( ), like Ebola. Example 2 represents a pathogen that has subcritical transmission in the recipient host ( ), like Nipah virus. In both examples, the donor and recipient life expectancies are set at 15 and 60 years, respectively, and birth rates are set to balance mortality rates ( ).

Example trajectories
Example 1: Figure S2: One random realization of dynamics for example system 1 ( ), with no interventions.
Example 2: Figure S3: One random realization of dynamics for example system 2 ( ), with no interventions. Figure S4: Total cases in the recipient population, as a function of the intensity (y-axis) of different ecological interventions (x-axis), for example system 1 (

Impact of interventions
). See Table S1 for parameter values used in this example. Figure S5: Number of spillover events (cases in the recipient population caused by donor-to-recipient transmission), as a function of the intensity (y-axis) of different ecological interventions (x-axis), for example system 1 ( ). Note that interventions that decrease recipient-to-recipient transmission without decreasing recipient susceptibility (i.e., behavior modification of the recipient, treatment of the recipient) can actually increase spillover relative to no management. This counterintuitive outcome occurs because these interventions reduce transmission within the recipient host, leaving more individuals susceptible to spillover. Thus, although there are more spillovers, there are fewer total cases in the recipient ( Figure S4).