John Cross, epidemic theory, and mathematically modeling the Norwich smallpox epidemic of 1819.

ABSTRACT: In this paper, we reintroduce Dr. John Cross' neglected and unusually complete historical data set describing a smallpox epidemic occurring in Norwich, England in 1819. We analyze this epidemic data in the context of early models of epidemic spread including the Farr-Evans-Brownlee Normal law, the Kermack-McKendrick square Hyperbolic Secant and SIR laws, along with the modern Volz-Miller random-network law. We show that Cross' hypothesis of susceptible pool limitation is sufficient to explain the data under the SIR law, but requires parameter estimates differing from the modern understanding of smallpox epidemiology or large errors in Cross' data collection. We hypothesize that these discrepancies are due to the mass-action hypothesis in SIR theory, rather than significant errors by Cross,

SUBMITTER: Olson CD 

PROVIDER: S-EPMC11560002 | biostudies-literature | 2024

REPOSITORIES: biostudies-literature