Open AccessTransmission dynamics and optimal control of a Huanglongbing model with time delay
Author(s) -
Zhenzhen Liao,
Shujing Gao,
Shen Yan,
Genjiao Zhou
Publication year - 2021
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2021209
Subject(s) - optimal control , uniqueness , control theory (sociology) , hopf bifurcation , pontryagin's minimum principle , mathematics , stability (learning theory) , maximum principle , transmission (telecommunications) , basic reproduction number , mathematical optimization , control (management) , bifurcation , computer science , mathematical analysis , physics , telecommunications , population , demography , nonlinear system , quantum mechanics , artificial intelligence , machine learning , sociology
In this paper, a mathematical model has been formulated for the transmission dynamics of citrus Huanglongbing considering latent period as the time delay factor. Existence of the equilibria and their stability have been studied on the basis of basic reproduction number in two cases τ=0 and τ>0. The results show that stability changes occur through Hopf bifurcation in the delayed system. Optimal control theory is then applied to investigate the optimal strategy for curtailing the spread of the disease using three time-dependent control variables determined from sensitivity analysis. By using Pontryagin's Maximum Principle, we obtain the optimal integrated strategy and prove the uniqueness of optimal control solution. Analytical and numerical findings suggest that it is feasible to implement control techniques while minimizing the cost of implementation of optimal control strategies.