辽宁工业大学学报（自然科学版）
遼寧工業大學學報（自然科學版）
료녕공업대학학보（자연과학판）
Journal of Liaoning Institute of Technology (Natural Science Edition)
2015年
5期
344-350
,共7页
传染病%治疗%发生率%平衡点%稳定性
傳染病%治療%髮生率%平衡點%穩定性
전염병%치료%발생솔%평형점%은정성
infectious diseases%treatment%incidence rate%equilibria%stability
考虑了具有双线性发生率和常数治疗函数的SIRS 传染病模型的动力学行为，并且研究了治疗能力对传染病传播的影响。通过数学分析得到无病平衡点与地方病平衡点存在性和稳定性的充分性判据。数值模拟表明，模型平衡点的存在性与稳定性不仅与基本再生数有关，而且与治疗能力也密切相关。同时显示当地方病平衡点不稳定时，采用适当的治疗就能够根治传染病。
攷慮瞭具有雙線性髮生率和常數治療函數的SIRS 傳染病模型的動力學行為，併且研究瞭治療能力對傳染病傳播的影響。通過數學分析得到無病平衡點與地方病平衡點存在性和穩定性的充分性判據。數值模擬錶明，模型平衡點的存在性與穩定性不僅與基本再生數有關，而且與治療能力也密切相關。同時顯示噹地方病平衡點不穩定時，採用適噹的治療就能夠根治傳染病。
고필료구유쌍선성발생솔화상수치료함수적SIRS 전염병모형적동역학행위，병차연구료치료능력대전염병전파적영향。통과수학분석득도무병평형점여지방병평형점존재성화은정성적충분성판거。수치모의표명，모형평형점적존재성여은정성불부여기본재생수유관，이차여치료능력야밀절상관。동시현시당지방병평형점불은정시，채용괄당적치료취능구근치전염병。
The global dynamics of an SIRS epidemic model with bilinear incidence rate and constant treatment rate of infectious individuals are considered, and the effect of the treatment capacity on spread is studied in this paper. By mathematical analysis, it gives the sufficient conditions for the existence and asymptotic stability of the diseasefree and endemic equilibria. By numerical simulations, it is shown that the existence and stability of equilibria for the model is not only related to the basic reproduction number, but also related to the treatment capacity. At the same time it shows that when the endemic equilibrium is unstable, appropriate treatment can cure infectious diseases.
