The network-level reproduction number and extinction threshold for vector-borne diseases

TL;DR

This paper explores the relationship between network-based reproduction numbers and extinction thresholds in vector-borne diseases, providing analytical and numerical insights to improve disease control strategies.

Contribution

It establishes relationships between reproduction numbers and extinction thresholds in network models, supported by numerical simulations and identifies key parameters affecting extinction probability.

Findings

Reproduction number is not monotonic with extinction threshold.

Numerical simulations align with analytical results.

Key parameters influencing extinction uncertainty are identified.

Abstract

The reproduction number of deterministic models is an essential quantity to predict whether an epidemic will spread or die out. Thresholds for disease extinction contribute crucial knowledge on disease control, elimination, and mitigation of infectious diseases. Relationships between the basic reproduction numbers of two network-based ordinary differential equation vector-host models, and extinction thresholds of corresponding continuous-time Markov chain models are derived under some assumptions. Numerical simulation results for malaria and Rift Valley fever transmission on heterogeneous networks are in agreement with analytical results without any assumptions, reinforcing the relationships may always exist and proposing a mathematical problem of proving their existences in general. Moreover, numerical simulations show that the reproduction number is not monotonically increasing or decreasing with the extinction threshold. Key parameters in predicting uncertainty of extinction thresholds are identified using Latin Hypercube Sampling/Partial Rank Correlation Coefficient. Consistent trends of extinction probability observed through numerical simulations provide novel insights into mitigation strategies to increase the disease extinction probability. Research findings may improve understandings of thresholds for disease persistence in order to control vector-borne diseases.