Modelling the Effect of Viruses on Insect Survival: Using a Second-Order Phase Transition Model to Describe Time–Effect and Dose–Effect Relationships Using Entomopathogenic Viruses as an Example

The present study examines the effect of viruses on forest insects depending on the virus dose. Two model approaches are used to quantify the effect of viruses on insect survival. Both approaches describe the processes of virus exposure to insects within the framework of the second-order phase transition model, which is well known in theoretical physics. The first approach examines the temporal dynamics of larval survival at a given dose of virus exposure. This dependence is characterized by the time-effect curve. In this case, the lethal time of exposure LT100 is the time required for the death of all larvae in the experiment at a given dose <i>D</i> of exposure. The second approach describes the relationship between the proportion <i>q_r</i> of larvae that survived a fixed time <i>T_c</i> after the start of the experiment and the dose <i>D</i> of virus exposure. This dependence is characterized by the dose-effect curve. The experiments tested the effect of two different viruses-nucleopolyhedrovirus (NPV) and cypovirus (CPV)-on such insect species as <i>Lymantria dispar</i> L., <i>Manduca sexta</i> L. and <i>Loxostege sticticalis</i> L. It was shown that the proposed models of second-order phase transitions very accurately (with coefficients of determination of the models close to <i>R</i>² = 0.95) describe experiments on studying the effect of different virus strains on insect survival. The proposed models turned out to be useful for assessing the effectiveness of different virus strains against insect pests. Since the parameters of the second-order "dose-time" and "dose-effect" phase transition models are related to each other, it is possible to reduce the number of measurements of virus-insect interaction due to the relationship between these parameters, and instead of <i>n</i> observations of insect dynamics over time depending on the dose of exposure, the basic parameters characterizing the "virus-insect" interactions can be accurately estimated using only one measurement. It appears that the proposed model can be used to calculate the effect of toxic agents on the population of victims for a wide variety of toxicant species and populations. A sharp reduction in the labor intensity of experiments to assess the toxicity of certain toxicants on animal populations will simplify and reduce the cost of testing the response of living objects to toxicants.