title: The schedule effect: can recurrent peak infections be reduced without vaccines, quarantines or school closings?
abstract: Using a basic, two transmission level seasonal SIR model, we introduce mathematical evidence for the schedule effect which asserts that major recurring peak infections can be significantly reduced by modification of the traditional school calendar. The schedule effect is observed first in simulated time histories of the infectious population. Schedules with higher average transmission rate may exhibit reduced peak infections. Splitting vacations changes the period of the oscillating transmission function and can confine limit cycles in the proportion susceptible/proportion infected phase plane. Numerical analysis of the phase plane shows the relationship between the transmission period and the maximum recurring infection peaks and period of the response. For certain transmission periods, this response may exhibit period-doubling and chaos, leading to increased peaks. Non-monotonic infectious response is also observed in conjunction with changing birth rate. We discuss how to take these effects into consideration to design an optimum school schedule with particular reference to a hypothetical developing world context.
authors.affiliation: Department of Mathematics, Wheaton College, Wheaton, IL 60187, USA. Electronic address: Danilo.Diedrichs@wheaton.edu.
authors.forename: Danilo R
authors.initials: DR
authors.lastname: Diedrichs
authors.affiliation: Department of Mathematics, Wheaton College, Wheaton, IL 60187, USA. Electronic address: Paul.Isihara@wheaton.edu.
authors.forename: Paul A
authors.initials: PA
authors.lastname: Isihara
authors.affiliation: Department of Mathematics, Wheaton College, Wheaton, IL 60187, USA. Electronic address: david.buursma@my.wheaton.edu.
authors.forename: Doeke D
authors.initials: DD
authors.lastname: Buursma
mesh_terms: D001723:Birth Rate; D002648:Child; D003140:Communicable Disease Control / Q000379:methods* / Q000706:statistics & numerical data; D018562:Disease Transmission, Infectious / Q000517:prevention & control / Q000706:statistics & numerical data; D006801:Humans; D007231:Infant, Newborn; D032541:Mass Vaccination; D055641:Mathematical Concepts; D008954:Models, Biological; D011790:Quarantine; D012574:Schools; D012621:Seasons; D013997:Time Factors
keywords: Period-doubling bifurcation; Phase plane; Schedule effect; Seasonal SIR model; Transmission function