关于“传染病学中的阈值定理”的进一步讨论

本文应用常微分方程稳定性理论、定性理论对两类传染病模型进行讨论,指出Kermack,W.O与Mckendrick,A.G早在1927年建立的著名的“传染病学中的阈值定理”之条件对其结论是不充分的,本文给出了正确的条件,并指出当这些条件不成立时最终患者人数的估计;文章还讨论了阈值的又一重意义,从而建立了相对于原阈值定理的“第二阈值定理”(本文称原阈值定理的“第一阈值定理”)。

THE THRESHOLD THEOREM OF EPIDEMIOLOGY

In 1927, W. O. Kermack and A. G. Mekendrick first gave the ThresholThreshold Theorem of Epidemiology. But the conditions presented in thatpaper was actually insufficient for the establishment of the conclusions of thetheorem. The present paper makes use of the stability theory and the qualitativetheory insolving this problem and reestablishes the Threshold Theorem ofEpidemiology. In addtion, this paper considers the revisionary model of(1), andpoints out that threshold-value has another meaning. Thus, the author of thepresent paper has defined the second Threshold Theorem of Epidemiology.