Sartwell's incubation period model revisited in the light of dynamic modeling

Abstract

The objective is to look into the well-known robustness of Sartwell's disease incubation period (IP) lognormal model. A new approach is proposed that embeds the pathogenesis of infection into the framework of percolation theory derived from the physical sciences. A two-step model of the individual disease process is proposed. The first step has a stochastic basis: it is aimed at establishing the threshold position of subjects bound to be diseased. Agent and host factors entertain and help the process reach the threshold. They include all the biologic risk factors (age, exposure dose and intensity, route of inoculation, etc.) to which Sartwell's model is usually found robust. The threshold is the point of no return of the disease process. The threshold provides the initial conditions of the second step. The second step traces the evolution of the pathologic process until disease onset: it is based on a nonlinear deterministic model that progressively unfolds the individual fates. As a chaotic regime is embedded into the model and as chaos unavoidably develops at some time entailing disease onset, the IP distribution becomes independent of the initial conditions laid out at the threshold. Unpredictable disease time courses and onsets are obtained. Biological examples supporting the model are provided. A simulation of 1000 pathologic processes is undertaken according to a simple birth-and-death process of microorganisms or cancer cells. As expected, a lognormal fits the IP distribution over a wide range. A lack of lengthy IPs is, however, observed. A simple multiplicative process coincides exactly with a lognormal model, but a multiplicative-competitive process such as that which is embedded in the nonlinear deterministic model has a narrower distribution. Large sample sizes are, however, needed to uncover this departure from the lognormal. Biologically, at least two phases of the empiric IP should be told apart: lengthy IPs should be distinguished from short and median IPs. Lengthy IPs emphasize interaction (complexity) between the disease progression and the immunological defenses of the host. Simulated distributions involving process complexity closely fit selected cancer data sets. Process complexity of the host pathologic unfolding can actually be recognized and quantified.