An epidemic model of a vector-borne disease with direct transmission and time delay |
| |
Authors: | Hui-Ming Wei Xue-Zhi Li |
| |
Institution: | a State Key Laboratory of Multiphase Flow in Power Engineering, Xi'an Jiaotong University, Xi'an 710049, China b Department of Mathematics, Xin Yang Normal University, Xin Yang 464000, China c Department of Mathematics, University of Florida, Gainesville, FL 32611-8105, USA |
| |
Abstract: | This paper considers an epidemic model of a vector-borne disease which has direct mode of transmission in addition to the vector-mediated transmission. The incidence term is assumed to be of the bilinear mass-action form. We include both a baseline ODE version of the model, and, a differential-delay model with a discrete time delay. The ODE model shows that the dynamics is completely determined by the basic reproduction number R0. If R0?1, the disease-free equilibrium is globally stable and the disease dies out. If R0>1, a unique endemic equilibrium exists and is locally asymptotically stable in the interior of the feasible region. The delay in the differential-delay model accounts for the incubation time the vectors need to become infectious. We study the effect of that delay on the stability of the equilibria. We show that the introduction of a time delay in the host-to-vector transmission term can destabilize the system and periodic solutions can arise through Hopf bifurcation. |
| |
Keywords: | Epidemic models Vector-borne disease Equilibrium analysis Stability Threshold Time delay Hopf bifurcation |
本文献已被 ScienceDirect 等数据库收录! |
|