Ricerche di Matematica

, Volume 67, Issue 1, pp 205–225 | Cite as

Time heterogeneous programs of vaccination awareness: modeling and analysis

  • B. Buonomo
  • N. Chitnis
  • A. d’Onofrio


We investigate the role of time heterogeneity of public health systems efforts in favoring the propensity of parents to vaccinate their newborns against a target childhood disease. The starting point of our investigation is the behavioral-epidemiology model proposed by d’Onofrio et al. (PLoS ONE 7:e45653, 2012), where the PHS effort was assumed to be constant. We also consider the co-presence of another layer of temporal heterogeneity: seasonality in the contact rate of the disease. We mainly assume that the effort is periodic with a 1-year period because of alternating working and holiday periods. We show that if the average effort is larger than a threshold, then the disease can be eliminated leading to an ideal equilibrium point with \(100\%\) of vaccinated newborns. A more realistic disease-free equilibrium can also be reached, under a condition that depends on the whole form of the time profile describing the PHS effort. We also generalize our disease elimination-related results to a wide class of time-heterogenous PHS efforts. Finally, we analytically show that if the disease elimination is not reached, then the disease remains uniformly persistent.


Infectious diseases Seasonality Vaccine Behavior Public health 

Mathematics Subject Classification

92D30 37B55 



The work of BB has been performed under the auspices of the Italian National Group for the Mathematical Physics (GNFM) of the National Institute for Advanced Mathematics (INdAM).


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Copyright information

© Università degli Studi di Napoli "Federico II" 2018

Authors and Affiliations

  1. 1.Department of Mathematics and ApplicationsUniversity of Naples Federico IINaplesItaly
  2. 2.Department of Public Health and EpidemiologySwiss Tropical and Public Health InstituteBaselSwitzerland
  3. 3.International Prevention Research InstituteLyonFrance
  4. 4.University of BaselBaselSwitzerland

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