Compartment Analysis of Disease Progression in Time. I. Unrestricted Disease Increase

Disease progression in time through presporulating (latent), sporulating (infectious) and postporulating (removal) stages has been modelled as a three‐compartment system in the case where no upper bound for total disease increase is considered. Deterministic compartment analysis has been performed based on Jeger's linked differential equations. Some important, well‐established epidemilogical principles and concepts have been ‘rediscovered’, clarified or redefined. A new variable, defined as total inoculum reservoir of the host, is suggested as an additional epidemiological concept. Three rate parameters with phytopathological meaning were included in the system: R the constant intrinsic infection rate comparable to the Vanderplankian R ,c , h pathogen's ‘hatching rate’, related to the mean latent period p and g the intrinsic removal rate related to the infectious period i. Another parameter λ 1 is empirical and comparable to the logarithmic, infection rate, sensu Vanderplank if time becomes very large. In the compartment system iR = 0 is a threshold condition for total disease to increase over initial disease level and iR = 1 is a threshold condition for an ‘explosive’ total disease increase that may induce a large epidemic rather than a threshold for total disease to start or to exist. When iR < 1, the total disease level approaches α asymptotically, a finite value, while when iR > 1, the total disease, increase is explosive; only where λ 1 =√d h does this increase follows the exponential law at larger t , otherwise the exponential law with the same rate parameter λ 1 underestimates or overstimates the amount of total disease at any time t. Some further implications are discussed and compared with those derived from the Vanderplankian system of epidemiological analysis.