多種傳播媒介的會完全復原的傳染模型之分析

Abstract

在這篇論文中我們提出與研究一個多重傳染媒介的SIS病毒傳播模型，在這個一般化的模型中人類之間的以異構的scale-free網絡作為連結方式，而人類與媒介間的連接方式我們則採用更一般化的網絡，如此一來具選擇性與不具選擇性的模型可以同時被我們討論、研究。我們的研究發現這個疾病疫情的模型可以用疾病再生指數 R0做分類、討論，並得出以下結果。若R0<1，則疾病疫情會消失，這表示人類與傳染媒介都痊癒。若R0>1，則疾病疫情會爆發，穩定收斂到一個穩定的平衡態。

In this paper, an epidemic SIS model (e.g.,rabies) with multiple infective media (e.g., dogs, ferret-Badgers and shrews) in complex networks is proposed and investigated. Such generalized model include a heterogeneous scale-free network between individuals and a generalized network between media and individuals. Such generalized networks is formulated in such a way so that both heterogeneous and homogeneous network are its special cases. The global dynamics of the model is studied rigorously. We compute the basic reproduction number R0 for our model and then show that if R0 < 1, then the disease-free equilibrium is globally asymptotically stable. On the contrary, if R0 > 1, then there exists a unique endemic equilibrium which is globally asymptotically stable.