title: Deterministic epidemiological models at the individual level.
abstract: In many fields of science including population dynamics, the vast state spaces inhabited by all but the very simplest of systems can preclude a deterministic analysis. Here, a class of approximate deterministic models is introduced into the field of epidemiology that reduces this state space to one that is numerically feasible. However, these reduced state space master equations do not in general form a closed set. To resolve this, the equations are approximated using closure approximations. This process results in a method for constructing deterministic differential equation models with a potentially large scope of application including dynamic directed contact networks and heterogeneous systems using time dependent parameters. The method is exemplified in the case of an SIR (susceptible-infectious-removed) epidemiological model and is numerically evaluated on a range of networks from spatially local to random. In the context of epidemics propagated on contact networks, this work assists in clarifying the link between stochastic simulation and traditional population level deterministic models.
authors.affiliation: Department of Mathematical Sciences, The University of Liverpool, Liverpool L69 7ZL, UK. kieran.sharkey@manchester.ac.uk
authors.forename: Kieran J
authors.initials: KJ
authors.lastname: Sharkey
mesh_terms: D002353:Carrier State / Q000453:epidemiology; D016000:Cluster Analysis; D003141:Communicable Diseases / Q000453:epidemiology*; D004196:Disease Outbreaks / Q000706:statistics & numerical data*; D018562:Disease Transmission, Infectious / Q000706:statistics & numerical data; D017753:Ecosystem; D004812:Epidemiologic Methods; D006801:Humans; D015233:Models, Statistical; D016571:Neural Networks, Computer; D011157:Population Dynamics; D013269:Stochastic Processes; D018511:Systems Integration; D013598:Systems Theory