TY - JOUR
T1 - A new mathematical model studying imperfect vaccination
T2 - Optimal control analysis
AU - Mohammed-Awel, Jemal
AU - Numfor, Eric
AU - Zhao, Ruijun
AU - Lenhart, Suzanne
N1 - Funding Information:
This work was partially supported through short term visits to the National Institute for Mathematical and Biological Synthesis, an Institute sponsored by the National Science Foundation through NSF Award # DBI-1300426 , with additional support from The University of Tennessee, Knoxville .
Publisher Copyright:
© 2021
PY - 2021/8/15
Y1 - 2021/8/15
N2 - In this study, a novel mathematical model is developed to investigate the effectiveness of imperfect human vaccination against malaria. The model is a system of ordinary differential equations (ODEs) coupled with a first-order partial differential equation (PDE) that describes transmission of malaria with time-since-vaccination structure for vaccinated humans. The existence and uniqueness of the solution to the system are established, the basic reproduction number (R0) is calculated, and model stability analysis of equilibria is performed. The optimal control problem, subject to the model system, is formulated with the optimal vaccination rate that minimizes the cost of implementing the imperfect vaccination as well as the number of infected humans. The optimality system is solved numerically, and several optimal control scenarios which effectively control the disease are presented.
AB - In this study, a novel mathematical model is developed to investigate the effectiveness of imperfect human vaccination against malaria. The model is a system of ordinary differential equations (ODEs) coupled with a first-order partial differential equation (PDE) that describes transmission of malaria with time-since-vaccination structure for vaccinated humans. The existence and uniqueness of the solution to the system are established, the basic reproduction number (R0) is calculated, and model stability analysis of equilibria is performed. The optimal control problem, subject to the model system, is formulated with the optimal vaccination rate that minimizes the cost of implementing the imperfect vaccination as well as the number of infected humans. The optimality system is solved numerically, and several optimal control scenarios which effectively control the disease are presented.
KW - Imperfect vaccine
KW - Malaria
KW - Optimal control
UR - http://www.scopus.com/inward/record.url?scp=85102584112&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85102584112&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2021.125132
DO - 10.1016/j.jmaa.2021.125132
M3 - Article
AN - SCOPUS:85102584112
SN - 0022-247X
VL - 500
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
M1 - 125132
ER -
