title: Perspectives on optimal control of varicella and herpes zoster by mass routine varicella vaccination.
abstract: Herpes zoster arises from reactivation of the varicella-zoster virus (VZV), causing varicella in children. As reactivation occurs when cell-mediated immunity (CMI) declines, and there is evidence that re-exposure to VZV boosts CMI, mass varicella immunization might increase the zoster burden, at least for some decades. Fear of this natural zoster boom is the main reason for the paralysis of varicella immunization in Europe. We apply optimal control to a realistically parametrized age-structured model for VZV transmission and reactivation to investigate whether feasible varicella immunization paths that are optimal in controlling both varicella and zoster exist. We analyse the optimality system numerically focusing on the role of the cost functional, of the relative zoster-varicella cost and of the planning horizon length. We show that optimal programmes will mostly be unfeasible for public health owing to their complex temporal profiles. This complexity is the consequence of the intrinsically antagonistic nature of varicella immunization programmes when aiming to control both varicella and zoster. However, we show that gradually increasing-hence feasible-vaccination schedules can perform better than routine programmes with constant vaccine uptake. Finally, we show the optimal profiles of feasible programmes targeting mitigation of the post-immunization natural zoster boom with priority.
authors.affiliation: Department of Information Engineering (DIE), University of Pisa, Via G. Caruso 16, 56122 Pisa, Italy monica.betta@for.unipi.it.
authors.forename: Monica
authors.identifier: http://orcid.org/0000-0002-5672-1638
authors.initials: M
authors.lastname: Betta
authors.affiliation: Institute of Life Sciences, Scuola Superiore Sant'Anna, Via Santa Cecilia 3, 56127 Pisa, Italy.
authors.forename: Marco
authors.identifier: http://orcid.org/0000-0003-4798-5196
authors.initials: M
authors.lastname: Laurino
authors.affiliation: Department of Mathematics, University of Trento, Via Calepina, 14, 38122 Trento, Italy.
authors.forename: Andrea
authors.identifier: http://orcid.org/0000-0002-3512-8560
authors.initials: A
authors.lastname: Pugliese
authors.affiliation: Bruno Kessler Foundation, Via S. Croce 77, 38122 Trento, Italy.
authors.forename: Giorgio
authors.identifier: http://orcid.org/0000-0002-9296-9470
authors.initials: G
authors.lastname: Guzzetta
authors.affiliation: Department of Information Engineering (DIE), University of Pisa, Via G. Caruso 16, 56122 Pisa, Italy.
authors.forename: Alberto
authors.identifier: http://orcid.org/0000-0002-0105-5121
authors.initials: A
authors.lastname: Landi
authors.affiliation: Department of Economics and Management, University of Pisa, Via Cosimo Ridolfi, 56122 Pisa, Italy.
authors.forename: Piero
authors.identifier: http://orcid.org/0000-0001-5853-8223
authors.initials: P
authors.lastname: Manfredi
mesh_terms: D000293:Adolescent; D000328:Adult; D002644:Chickenpox / Q000517:prevention & control* / Q000821:virology; D002648:Child; D002675:Child, Preschool; D005060:Europe; D006562:Herpes Zoster / Q000517:prevention & control* / Q000821:virology; D014645:Herpesvirus 3, Human / Q000276:immunology*; D006801:Humans; D032541:Mass Vaccination; D008875:Middle Aged; D008962:Models, Theoretical; D055815:Young Adult
keywords: herpes zoster; immunity boosting; mass vaccination; optimal control; varicella