Open AccessGlobal dynamics and optimal control of a cholera transmission model with vaccination strategy and multiple pathways
Author(s) -
Chenwei Song,
Rui Xu,
Na Bai,
Xiao Hong Tian,
Jia Lin
Publication year - 2020
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.2020233
Subject(s) - basic reproduction number , optimal control , transmission (telecommunications) , vaccination , cholera , pontryagin's minimum principle , maximum principle , mathematics , sanitation , quarantine , mathematical optimization , control (management) , stability theory , epidemic model , control theory (sociology) , mathematical economics , computer science , biology , demography , virology , medicine , ecology , population , physics , sociology , telecommunications , pathology , artificial intelligence , nonlinear system , quantum mechanics
In this paper, we consider a cholera infection model with vaccination and multiple transmission pathways. Dynamical properties of the model are analyzed in detail. It is shown that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than unity; the endemic equilibrium exists and is globally asymptotically stable if the basic reproduction number is greater than unity. In addition, the model is successfully used to fit the real disease situation of cholera outbreak in Somalia. We consider an optimal control problem of cholera transmission with vaccination, quarantine, treatment and sanitation control strategies, and use Pontryagin's minimum principle to determine the optimal control level. The optimal control problem is solved numerically.