多宿主－多寄生者系の共進化における赤の女王のダイナミクス

博士(理学)doctoral創造科学技術大学院静岡大学甲第912号ET

A Mathematical Model of Intra-Colony Spread of American Foulbrood in European Honeybees (<i>Apis mellifera</i> L.)

<div><p>American foulbrood (AFB) is one of the severe infectious diseases of European honeybees (<i>Apis mellifera</i> L.) and other <i>Apis</i> species. This disease is caused by a gram-positive, spore-forming bacterium <i>Paenibacillus larvae</i>. In this paper, a compartmental (SI framework) model is constructed to represent the spread of AFB within a colony. The model is analyzed to determine the long-term fate of the colony once exposed to AFB spores. It was found out that without effective and efficient treatment, AFB infection eventually leads to colony collapse. Furthermore, infection thresholds were predicted based on the stability of the equilibrium states. The number of infected cell combs is one of the factors that drive disease spread. Our results can be used to forecast the transmission timeline of AFB infection and to evaluate the control strategies for minimizing a possible epidemic.</p></div

Description of the state variables.

<p>Description of the state variables.</p

The compartmental diagram of the interaction of bees and the spread of AFB spores within a colony.

<p>The red arrows indicate infection while the blue arrows indicate transition of states (refer to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0143805#pone.0143805.t001" target="_blank">Table 1</a> for the definition of the state variables).</p

The trajectory of the state variable <i>B</i>, <i>B</i>_<i>a</i> and <i>B</i>_<i>s</i> versus the state variable <i>C</i> with initial condition (0,0,0,0,0,10000,0) and parameters.

<p><i>L</i> = 1500, <i>w</i> = 21000, <i>v</i> = 10000, <i>α</i>₄ = 1/3, <i>α</i>₃ = 0.001, <i>α</i>₂ = 1, <i>α</i>₁ = 0.001, <i>φ</i>₁ = 1/3, <i>φ</i>₂ = 1/3, <i>σ</i> = 0.001, <i>β</i>₁ = 1/3, <i>β</i>₂ = 1/15, and <i>μ</i> = 1/30.</p

The trajectory of the system Eq (7) with initial condition (0,0,0,1,10000,0) and parameters <i>L</i> = 1500, <i>w</i> = 21000, <i>v</i> = 10000, <i>α</i>₄ = 0, <i>α</i>₃ = 0.0005, <i>α</i>₂ = 1, <i>α</i>₁ = 0.001, <i>φ</i>₁ = 1/3, <i>φ</i>₂ = 1, <i>σ</i> = 0.001, <i>β</i>₁ = 1/5, <i>β</i>₂ = 1/13, and <i>μ</i> = 1/30.

<p>This figure shows that the colony dies out if one of the cell combs is already contaminated with spores.</p