# 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

## TL;DR

This study uses physics-based models to predict how viruses kill forest insects, accurately estimating insect death rates with high precision.

## Contribution

The study introduces a novel physics-inspired model using second-order phase transitions to describe virus-insect interactions with high accuracy.

## Key findings

- The proposed models accurately predict insect death rates with 95% accuracy.
- The models reduce the number of required experiments by linking dose-time and dose-effect parameters.
- The approach is applicable to various viruses and insect species.

## Abstract

This study explores how viruses can control forest insects by examining how the amount of virus and exposure time affect insect death rates. The goal was to create simple mathematical models to predict how well viruses work against insect pests. Researchers tested two entomopathogenic viruses (nucleopolyhedrovirus and cypovirus) and found that their models accurately predict insect deaths (with a high accuracy of 95%) depending on treatment doses. These models use ideas from physics to describe how viruses impact insects, similar to how physical systems change states. By using just one experiment, the models can estimate how effective different virus strains are at killing pests. The findings are valuable because they offer a way to estimate effective doses using a low amount of tested doses compared to the commonly used probit- or logit-based analysis approaches.

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 D of exposure. The second approach describes the relationship between the proportion qr of larvae that survived a fixed time Tc after the start of the experiment and the dose D 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 Lymantria dispar L., Manduca sexta L. and Loxostege sticticalis L. It was shown that the proposed models of second-order phase transitions very accurately (with coefficients of determination of the models close to R2 = 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 n 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.