Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (5): 1260-1271.

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Stability of Age-Structured with Proportion of Infected Groups or Enter the Latent Epidemiological Model with Varying Population Size

Gaixia Wang1(),Jixuan Liu2(),Xuezhi Li3   

  1. 1 College of Mathematics and Information, Xinyang University, Henan Xinyang 464000
    2 Basic Department, Aeronautic Sergeant College of Air Force Engingeering University, Henan Xinyang 464000
    3 College of Mathematics and Information Science, Henan Normal University, Henan Xinxiang 453007
  • Received:2017-06-09 Online:2019-10-26 Published:2019-11-08
  • Supported by:
    the NSFC(11271314);the Key Scientific Research Projects in Colleges and Universities of Henan Province(17A110030);the Training Program for Young Key Teachers in Institutions of Higher Learning of Henan Province(2018GGJS198)


Due to the influence of age or physical fitness, resulting in a number of susceptible to infection into the latent, some directly into patients, study of epidemic model so it is necessary to enter a latent or infected population proportion, but this kind of model is rarely taken into account the influence of age, study on the age structure of the infectious disease model of this change on the proportion of the total population in infected groups or latent, the expressions of the threshold parameters related to the population growth index are obtained, the existence and the local asymptotic stability conditions of the disease-free equilibrium and endemic equilibrium are discussed, then, the use of these conditions to control the spread of disease has important theoretical and practical significance.

Key words: Proportion, Varying population size, Spectrum

CLC Number: 

  • O175.12