TY - JOUR
ID - 6843
TI - An investigation into the optimal control of the horizontal and vertical incidence of communicable infectious diseases in society
JO - Journal of Mathematical Modeling
JA - JMM
LA - en
SN - 2345-394X
AU - Akbari, Reza
AD - Department of Mathematics, Payame Noor Unvierstiy, Tehran, Irann
Y1 - 2023
PY - 2023
VL - 11
IS - 4
SP - 605
EP - 616
KW - optimal control
KW - infectious diseases
KW - basic reproduction number
KW - Stability
KW - Mathematical model
DO - 10.22124/jmm.2023.23774.2122
N2 - This article aims at proposing and developing a three-component mathematical model for susceptible, infected and recovered $(SIR)$ population, under the control of vaccination of the susceptible population and drug therapy (antivirus) of the infected population (patient) in case of an infectious disease. The infectious disease under study can be transmitted through direct contact with an infected person (horizontal transmission) and from parent to child (vertical transmission). We investigate the basic reproduction number of the mathematical model, the existence and local asymptotic stability of both the disease free and endemic equilibrium. Using Pontryagin's minimum principle, we investigate the conditions of reducing the susceptible and infected population and increasing the recovered population based on the use of these two controllers in society. A numerical simulation of the optimal control problem shows, using both controllers is much more effective and leads to a rapid increase in the recovered population and prevents the disease from spreading and becoming an epidemic inthe society.
UR - https://jmm.guilan.ac.ir/article_6843.html
L1 - https://jmm.guilan.ac.ir/article_6843_b25a7fc55abaf6dc592b327847e30e3b.pdf
ER -