Differential Modeling of the Processes of Spreading and Elimination of Infectious Diseases of Forest Plantations

Abstract

The destabilization of the sustainable state of forests and the associated deterioration of the sanitary climate are mainly associated with their diseases. One of the main tasks of forest pathology monitoring is the detection of foci of disease of stands and the fight against their spread. In this paper, we propose a mathematical description of the processes of the spread and elimination of infectious diseases of forest plantations using the deterministic SIR (Susceptible, Infected, Recovered) model, the main provisions of which are basic in the interpretation of various kinds of infectious diseases, often taking the form of epidemics. Assuming the constancy of the total number of healthy infected subjects during the spread of the disease and the direct proportional dependence of the infection rate on the number of infected, the results obtained indicate that: a) if at the initial moment of time the number of infected individuals does not exceed a certain deterministic value, then plants do not become infected over time; b) in cases if this number is greater than a fixed value, then the part of individuals susceptible to the disease will become infected. It is shown that despite the abstract nature and the impossibility of probabilistic interpretation of the detection of foci of the disease, the proposed differential model can be effective in solving the problems of the spread, localization and prediction of tree diseases and is used, practically, for any closed biological and ecological system