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An Empirically-parametrized Spatio-Temporal Extended-SIR Model for Combined Dilution and Vaccination Mitigation for Rabies Outbreaks in Wild Jackals

Teddy Lazebnik, Yehuda Samuel, Jonathan Tichon, Roi Lapid, Roni King, Tomer Nissimian, Orr Spiegel

TL;DR

This study develops an empirically-parametrized spatio-temporal extended-SIR model with a graph-based spatial framework and agent-based simulation to study rabies spread in wild jackals. Parameterization relies on ATLAS telemetry from the Harod Valley in Israel, enabling realistic exploration of how vaccination and non-selective population-dilution interventions interact across space. The results show that vaccination consistently reduces transmission metrics (e.g., $E[R_t]$), while dilution can counterproductively increase spread under certain ecological conditions, with movement/dispersal between activity centers emerging as a stronger driver than population size. The work highlights the need for movement-aware, coordinated EIP strategies within OneHealth, and provides a methodological blueprint for evaluating multi-policy interventions in wildlife epizootics.

Abstract

The transmission of zoonotic diseases between animals and humans poses an increasing threat. Rabies is a prominent example with various instances globally, facilitated by a surplus of meso-predators (commonly, facultative synanthropic species e.g., golden jackals [Canis aureus, hereafter jackals]) thanks to the abundance of anthropogenic resources leading to dense populations close to human establishments. To mitigate rabies outbreaks and prevent human infections, authorities target the jackal which is the main rabies vector in many regions, through the dissemination of oral vaccines in known jackals' activity centers, as well as opportunistic culling to reduce population density. Because dilution (i.e., culling) is not selective towards sick or un-vaccinated individuals, these two complementary epizootic intervention policies (EIPs) can interfere with each other. Nonetheless, there is only limited examination of the interactive effectiveness of these EIPs and their potential influence on rabies epizootic spread dynamics, highlighting the need to understand these measures and the spread of rabies in wild jackals. In this study, we introduce a novel spatio-temporal extended-SIR (susceptible-infected-recovered) model with a graph-based spatial framework for evaluating mitigation efficiency. We implement the model in a case study using a jackal population in northern Israel, and using spatial and movement data collected by Advanced Tracking and Localization of Animals in real-life Systems (ATLAS) telemetry. An agent-based simulation approach allows us to explore various biologically-realistic scenarios, and assess the impact of different EIPs configurations. Our model suggests that under biologically-realistic underlying assumptions and scenarios, the effectiveness of both EIPs is not influenced much by the jackal population size but is sensitive to their dispersal between activity centers.

An Empirically-parametrized Spatio-Temporal Extended-SIR Model for Combined Dilution and Vaccination Mitigation for Rabies Outbreaks in Wild Jackals

TL;DR

This study develops an empirically-parametrized spatio-temporal extended-SIR model with a graph-based spatial framework and agent-based simulation to study rabies spread in wild jackals. Parameterization relies on ATLAS telemetry from the Harod Valley in Israel, enabling realistic exploration of how vaccination and non-selective population-dilution interventions interact across space. The results show that vaccination consistently reduces transmission metrics (e.g., ), while dilution can counterproductively increase spread under certain ecological conditions, with movement/dispersal between activity centers emerging as a stronger driver than population size. The work highlights the need for movement-aware, coordinated EIP strategies within OneHealth, and provides a methodological blueprint for evaluating multi-policy interventions in wildlife epizootics.

Abstract

The transmission of zoonotic diseases between animals and humans poses an increasing threat. Rabies is a prominent example with various instances globally, facilitated by a surplus of meso-predators (commonly, facultative synanthropic species e.g., golden jackals [Canis aureus, hereafter jackals]) thanks to the abundance of anthropogenic resources leading to dense populations close to human establishments. To mitigate rabies outbreaks and prevent human infections, authorities target the jackal which is the main rabies vector in many regions, through the dissemination of oral vaccines in known jackals' activity centers, as well as opportunistic culling to reduce population density. Because dilution (i.e., culling) is not selective towards sick or un-vaccinated individuals, these two complementary epizootic intervention policies (EIPs) can interfere with each other. Nonetheless, there is only limited examination of the interactive effectiveness of these EIPs and their potential influence on rabies epizootic spread dynamics, highlighting the need to understand these measures and the spread of rabies in wild jackals. In this study, we introduce a novel spatio-temporal extended-SIR (susceptible-infected-recovered) model with a graph-based spatial framework for evaluating mitigation efficiency. We implement the model in a case study using a jackal population in northern Israel, and using spatial and movement data collected by Advanced Tracking and Localization of Animals in real-life Systems (ATLAS) telemetry. An agent-based simulation approach allows us to explore various biologically-realistic scenarios, and assess the impact of different EIPs configurations. Our model suggests that under biologically-realistic underlying assumptions and scenarios, the effectiveness of both EIPs is not influenced much by the jackal population size but is sensitive to their dispersal between activity centers.
Paper Structure (19 sections, 10 equations, 7 figures, 1 table)

This paper contains 19 sections, 10 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methods and Materials
  3. Model definition
  4. Epizootic intervention policies
  5. Agent based simulation
  6. Epizootic intervention policy optimization procedure
  7. Spatio-temporal data fitting procedure
  8. Epizootic spread metrics
  9. Theoretical analysis
  10. Solution existence and uniqueness
  11. Epizootic intervention policies effect
  12. Experiments
  13. Data acquisition and experimental setup
  14. Setup
  15. Results
  16. ...and 4 more sections

Figures (7)

  • Figure 1: A schematic view of the proposed model. The left panel shows the temporal-epidemiological dynamics according to an SEI model. The right panel shows a graph-based spatial representation of the population with 4 activity centers, each with $J_i$ jackals, and $F_i$ food. Dashed lines represent emigration (dispersal) among centers.
  • Figure 2: A schematic view of the temporal interaction in the model, including the vaccination and population dilution EIPs.
  • Figure 3: A comparison between different EIP strategies in terms of the three epizootic spread metrics. The results are shown as the mean $\pm$ standard deviation of $n=100$ repetitions.
  • Figure 4: The influence of population size (the x-axis) and immigration rate (y-axis, i.e., dispersal between activity centers) on the epizootic spread under an optimal EIP configuration. The results are shown as the mean of $n=100$ repetitions for each configuration (no EIP, vaccination only, and dilution only) with warmer colors indicating higher values of epizootic indices for ARN, MI, and PDI in the three respective rows.
  • Figure 5: The influence of different EIP combinations under the optimal configuration. The results are shown as the mean of $n=100$ repetitions for each configuration.
  • ...and 2 more figures