Analysis of Varroosis Model in Honeybee Colony with Interventions

Abstract

A deterministic mathematical model is proposed and analyzed to study the transmission dynamics of Varroosis in honeybee colony with interventions. The study combined both treatment and biocontrol strategy on curbing the menace of Varroosis on honeybee colony. As such, the study established the existence of the most important four steady states that include: disease-free and infestation-free, infestation with virus-free Varroa-mites, infestation with virus-carrying Varroa-mites and endemic steady state. Moreover, the study established the existence of backward bifurcation and sensitivity analysis of the model was performed. Correspondingly, the analysis of the model reveals that, ineffective treatment can induce backward bifurcation. Furthermore, the study results indicated that, when treatment is 100% effective, the disease-free and infestation-free steady state is globally asymptotically stable for R0 1the global stability of the endemic steady state is proved only on a special case.

Keywords

• bifurcation, global stability, sensitivity analysis and honeybee colony