Mathematical Model Analysis of Honey Bee Population in the Presence of Virus Infection where Broods Follow Logistic Growth

Abstract

Honeybees (Apis mellifera) play a vital role as pollinators of key crops in agriculture. They produce honey and beeswax for nutritional and industrial uses. Infectious diseases caused by viruses pose a significant threat to their colonies and biodiversity, which requires investigation.  In this paper, we develop and present a deterministic SIRS mathematical model that effectively captures the population dynamics of honeybee colonies impacted by viral infections, incorporating new assumptions and parameters into established models. The qualitative behavior of honeybee-pathogen interactions shows that whenever the survivability of a newly hatched egg is guaranteed, both the disease-free and endemic equilibria of the model are locally asymptotically stable with some conditions on parameters. According to the analysis of the model qualitative behavior of honeybee-virus interactions shows that whenever the survivability of newly hatched eggs is maintained, the disease-free and endemic equilibria of the model are locally asymptotically stable with some conditions on parameters. Disease-free and endemic equilibria are globally asymptotically stable. The basic reproduction number  is determined using the next-generation matrix method, and sensitivity analysis shows that virus transmission rates are the most influential parameters. Numerical simulations for different scenarios are performed using MATLAB software and the outcomes describe the significance of model parameters, such as the net growth rate of brood and rate of maturation.