Using Hawkes Processes to model imported and local malaria cases in near-elimination settings.

H Juliette T Unwin,Marian-Andrei Rizoiu,Swapnil Mishra,Samir Bhatt,Shengjie Lai,Seth Flaxman,Isobel Routledge,Daniel J Weiss,Justin Cohen

doi:10.1371/journal.pcbi.1008830

Abstract

Developing new methods for modelling infectious diseases outbreaks is important for monitoring transmission and developing policy. In this paper we propose using semi-mechanistic Hawkes Processes for modelling malaria transmission in near-elimination settings. Hawkes Processes are well founded mathematical methods that enable us to combine the benefits of both statistical and mechanistic models to recreate and forecast disease transmission beyond just malaria outbreak scenarios. These methods have been successfully used in numerous applications such as social media and earthquake modelling, but are not yet widespread in epidemiology. By using domain-specific knowledge, we can both recreate transmission curves for malaria in China and Eswatini and disentangle the proportion of cases which are imported from those that are community based.

Highlights

Modelling infectious disease transmission is an important tool for monitoring outbreaks and developing public policy to limit the spread of the disease
This paper introduces a mathematically well-founded method for infectious disease outbreaks known as Hawkes Processes
These semi-mechanistic models are relatively new to the infectious diseases toolkit and enable us to combine disease specific information such as the infectious profile with statistical rigour to recreate temporal disease transmission

Summary

Introduction

Modelling infectious disease transmission is an important tool for monitoring outbreaks and developing public policy to limit the spread of the disease. SIR (Susceptible—Infected—Recovered) type models, such as the seminal Kermack-McKendrick model [1], or individual-based models (for example [2] and [3]) have been used to model disease outbreaks These methods encode well-known disease-specific mechanisms and can produce very good fits to data. An alternative method proposed by Routledge et al [4, 5] estimates temporal and spatial reproduction numbers by studying information diffusion processes in the form of network models, which reconstruct information transmission using known or inferred times of infection in a Bayesian framework [6] These methods provide an adaptable framework to integrate multiple data types at different scales and identify missing data or external infection sources, but require very good data sets to accurately be able to predict from the models [6, 7]. The intensity of the Hawkes Processes is a stochastic function because it depends on event times which are random variables, the Hawkes Process can be treated as a non-homogeneous Poisson

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