﻿ 浓核病毒HaDNV-1在棉铃虫种群中传播的数学模型 Modeling the Transmission of Densovirus (HaDNV-1) in the Helicoverpa armigera Population

Vol.05 No.02(2016), Article ID:17556,13 pages
10.12677/AAM.2016.52031

Modeling the Transmission of Densovirus (HaDNV-1) in the Helicoverpa armigera Population

Shuting Chen, Zhiming Guo

School of Mathematics and Information Science, Guangzhou University, Guangzhou Guangdong

Received: Apr. 23rd, 2016; accepted: May 10th, 2016; published: May 13th, 2016

ABSTRACT

Densovirus (HaDNV-1) is a mutualistic symbiont of Helicoverpa armigera, and the infected females occupy advantage in vertical transmission. A model of species competition was posed to understand the influence of HaDNV-1. When the damage of HaDNV-1 is neglected, the stability of equilibria was analysed and a conclusion was drawn that the infected is dominant in Helicoverpa armigera population. Considering the harm of HaDNV-1, the model was modified by raising the mortality of the infected adult and larva respectively to indicate the cost; thereby the mortality was evaluated to lead to the infected pests extinct.

Keywords:Species Competition, Mutualistic Symbiont, Female Transmission Advantage, Stability

1. 引言

Table 1. The vertical transmission of HaDNV-1

2. 基础模型

(2.1)

(2.2)

(2.3)

3. 系统(2.3)平衡点的稳定性

(3.1)

。即系统(3.1)不存在正平衡点。

(ii) 当时，系统(3.1)存在边界平衡点，且是一个局部渐近稳定的结点；

(iii) 系统(3.1)不存在正平衡点。

(4.1)

(ii) 假设。若，则是局部渐近稳定的。

(H1)成立等价于

(4.2)

(4.3)

Table 2. The type of equilibria of system (4.1)

(ii) 假设。若

，因此

(i) 如果，则

(ii) 如果，则

(ii) 假设。若，则全局渐近稳定；

(iii) 若，则全局渐近稳定。

(ii)和(iii)同样用引理(4.1)可以证得，证毕。

5. 总结与讨论

Modeling the Transmission of Densovirus (HaDNV-1) in the Helicoverpa armigera Population[J]. 应用数学进展, 2016, 05(02): 242-254. http://dx.doi.org/10.12677/AAM.2016.52031

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