Modeling spatial invasion of Ebola in West Africa, JP D'Silva and MC Eisenberg, Journal of Theoretical Biology, 2017. This paper uses a "gravity" spatial mode to look at how spatial transmission contributed to the 2014-2016 Ebola outbreak. In short, we argue that one region (country or district) can act as a case reservoir, exacerbating the outbreak in neighbouring regions (through transmission between regions), and that intervention targeted to specific regions can have significant effects on the epidemic as a whole by reducing this inter-region transmission. The country-level model fits the cumulative incidence of the outbreak surprisingly well, especially the multiple exponential phases of the outbreak in Guinea.
Constructing a Simple Hybrid Model of Perineural Invasion, JP D'Silva and MC Eisenberg. This report, from the 2017 UMich Math REU, contains some of our early work on modelling the interaction between oral cancer and nerves (perineural invasion). I talked about a much updated version of this work (an entirely different mathematical model structure) at IADR 2018; a pre-print is coming soon.
Identifiability of linear compartmental models of
infectious disease transmission, JP D'Silva and MC Eisenberg, 2018. In this report, we study the identifiability of deterministic stage-structured infection models (SEIR with multiple I compartments). We first prove that they are unidentifiable. Then, we obtain the identifiable combinations for the case where all stages have equal lengths, and conjecture the identifiable combinations for the general case. Finally, we make progress towards proving the conjecture.