@article { , title = {The deterministic Kermack?McKendrick model bounds the general stochastic epidemic}, abstract = {We prove that, for Poisson transmission and recovery processes, the classic Susceptible \$\\to\$ Infected \$\\to\$ Recovered (SIR) epidemic model of Kermack and McKendrick provides, for any given time \$t>0\$, a strict lower bound on the expected number of suscpetibles and a strict upper bound on the expected number of recoveries in the general stochastic SIR epidemic. The proof is based on the recent message passing representation of SIR epidemics applied to a complete graph.}, doi = {10.1017/jpr.2016.62}, issn = {0021-9002}, issue = {4}, journal = {Journal of Applied Probability}, pages = {1031-1040}, publicationstatus = {Published}, publisher = {Applied Probability Trust}, url = {https://nottingham-repository.worktribe.com/output/835942}, volume = {53}, keyword = {General stochastic epidemic, deterministic general epidemic, SIR, Kermack-McKendrick, message passing, bound}, year = {2016}, author = {Wilkinson, Robert R. and Ball, Frank G. and Sharkey, Kieran J.} }