Journal
JOURNAL OF MATHEMATICAL BIOLOGY
Volume 77, Issue 5, Pages 1299-1339Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00285-018-1253-7
Keywords
Homogeneous dynamical system; Demographic transition; Epidemic models; Basic reproduction number
Categories
Funding
- Japan Society for the Promotion of Science (JP) [16K05266] Funding Source: Medline
- Grants-in-Aid for Scientific Research [16K05266] Funding Source: KAKEN
Ask authors/readers for more resources
In this paper, we formulate an age-structured epidemic model for the demographic transition in which we assume that the cultural norms leading to lower fertility are transmitted amongst individuals in the same way as infectious diseases. First, we formulate the basic model as an abstract homogeneous Cauchy problem on a Banach space to prove the existence, uniqueness, and well-posedness of solutions. Next based on the normalization arguments, we investigate the existence of nontrivial exponential solutions and then study the linearized stability at the exponential solutions using the idea of asynchronous exponential growth. The relative stability defined in the normalized system and the absolute (orbital) stability in the original system are examined. For the boundary exponential solutions corresponding to infection-free or totally infected status, we formulate the stability condition using reproduction numbers. We show that bi-unstability of boundary exponential solutions is one of conditions which guarantee the existence of coexistent exponential solutions.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available