TY - JOUR
T1 - Qualitative analysis and optimal control of an epidemic model with vaccination and treatment
AU - Buonomo, Bruno
AU - Lacitignola, Deborah
AU - Vargas-De-León, Cruz
PY - 2014/6
Y1 - 2014/6
N2 - We focus on an epidemic model which incorporates a non-linear force of infection and two controls: an imperfect preventive vaccine given to susceptible individuals and therapeutic treatment given to infectious. We study both the cases of constant and non constant controls. In the case of constant controls we perform a qualitative analysis based on Lyapunov stability which allows to integrate the bifurcation analysis performed in a previous paper. The occurrence of a backward bifurcation is discussed in the perspective of disease control. The case of time-dependent controls is studied by means of the optimal control theory. The strategy is to minimize both the disease burden and the intervention costs. We derive the optimality system and solve it numerically. The characterization of the optimal time profile of the controls, together with the qualitative analysis provides a rather complete picture of the possible outcomes of the model.
AB - We focus on an epidemic model which incorporates a non-linear force of infection and two controls: an imperfect preventive vaccine given to susceptible individuals and therapeutic treatment given to infectious. We study both the cases of constant and non constant controls. In the case of constant controls we perform a qualitative analysis based on Lyapunov stability which allows to integrate the bifurcation analysis performed in a previous paper. The occurrence of a backward bifurcation is discussed in the perspective of disease control. The case of time-dependent controls is studied by means of the optimal control theory. The strategy is to minimize both the disease burden and the intervention costs. We derive the optimality system and solve it numerically. The characterization of the optimal time profile of the controls, together with the qualitative analysis provides a rather complete picture of the possible outcomes of the model.
KW - Backward bifurcation
KW - Epidemic model
KW - Global stability
KW - Optimal control
KW - Vaccination
UR - http://www.scopus.com/inward/record.url?scp=84897067572&partnerID=8YFLogxK
U2 - 10.1016/j.matcom.2013.11.005
DO - 10.1016/j.matcom.2013.11.005
M3 - Artículo
SN - 0378-4754
VL - 100
SP - 88
EP - 102
JO - Mathematics and Computers in Simulation
JF - Mathematics and Computers in Simulation
ER -