TY - JOUR
AU - Liu, Kaiyuan
AU - Zhang, Tongqian
AU - Chen, Lansun
PY - 2019
DA - 2019/02/06
TI - State-Dependent Pulse Vaccination and Therapeutic Strategy in an SI Epidemic Model with Nonlinear Incidence Rate
SP - 3859815
VL - 2019
AB - In this paper, the state-dependent pulse vaccination and therapeutic strategy are considered in the control of the disease. A pulse system is built to model this process based on an SI ordinary differential equation model. At first, for the system neglecting the impulse effect, we give the classification of singular points. Then for the pulse system, by using the theory of the semicontinuous dynamic system, the dynamics is analyzed. Our analysis shows that the pulse system exhibits rich dynamics and the system has a unique order-1 homoclinic cycle, and by choosing p as the control parameter, the order-1 homoclinic cycle disappears and bifurcates an orbitally asymptotical stable order-1 periodic solution when p changes. Numerical simulations by maple 18 are carried out to illustrate the theoretical results.
SN - 1748-670X
UR - https://doi.org/10.1155/2019/3859815
DO - 10.1155/2019/3859815
JF - Computational and Mathematical Methods in Medicine
PB - Hindawi
KW -
ER -