Journal
COMPUTATIONAL & APPLIED MATHEMATICS
Volume 37, Issue 4, Pages 4055-4080Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s40314-017-0560-8
Keywords
Vector-borne disease model; Infection age; General incidence rate; Uniform persistence; Fluctuation lemma; Lyapunov functional
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Funding
- NSFC [11771374, 11471089]
- CSC [201508410281]
- Nanhu Scholar Program for Young Scholars of Xinyang Normal University
- Program for Science and Technology Innovation Talents in Universities of Henan Province [17HASTIT011]
- Universities Young Teachers Program of Henan Province [2014GGJS-093]
- NSERC
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A vector-borne disease model with general incidence rates is proposed and investigated in this paper, where both vector and host are stratified by infection ages in the form of a hyperbolic system of partial differential equations coupled with ordinary differential equations. The existence, uniqueness, nonnegativeness, and boundedness of solution of the model are studied for biologically reasonable purpose. Furthermore, a global threshold dynamics of the system is established by constructing suitable Lyapunov functionals, which is determined by the basic reproduction number : the infection-free equilibrium is globally asymptotically stable when while the endemic equilibrium is globally asymptotically stable when .
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