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Dynamics and optimal control of an age‐structured SIRVS epidemic model
Author(s) -
Duan XiChao,
Jung I Hyo,
Li XueZhi,
Martcheva Maia
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6190
Subject(s) - vaccination , epidemic model , pontryagin's minimum principle , basic reproduction number , optimal control , mathematics , immunity , maximum principle , mathematical modelling of infectious disease , disease , infectious disease (medical specialty) , mathematical optimization , medicine , immunology , immune system , population , environmental health , pathology
Vaccination and treatment are both effective methods of preventing the spread of infectious diseases. In this paper, we propose an SIRVS epidemic model with ages of vaccination and recovery, involving vaccine‐induced immunity and infection‐induced immunity. The basic reproduction number of the epidemic model,R 0 , is first obtained. IfR 0 < 1 , the local and global stabilities of the disease‐free steady state are strictly proved. IfR 0 > 1 , to control the disease, an optimal control problem is discussed by evaluating the cost of control strategies (vaccination and treatment) and using Pontryagin's maximum principle. We use specific parameter values related to influenza A to do some numerical simulations. Results show that the recovery age plays an important role in the optimal control, where precisely, the control with vaccination only has no effect when the acquired immunity period is not more than the vaccination immunity period; otherwise, it plays a significant role in disease control.