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

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.
Author summary 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. We show that these methods are very suited to modelling malaria in communities close to eliminating malaria—in particular China and Eswatini—where we are able to disentangle the contribution of exogenous (external) transmission and endogenous (person-to-person) transmission. This is particularly important for developing policies when counties are approaching elimination.