Preprint Article Version 1 This version is not peer-reviewed

Integer Versus Fractional Order SEIR Deterministic and Stochastic Models of Measles

Version 1 : Received: 25 January 2020 / Approved: 26 January 2020 / Online: 26 January 2020 (03:38:06 CET)

A peer-reviewed article of this Preprint also exists.

Islam, M.R.; Peace, A.; Medina, D.; Oraby, T. Integer Versus Fractional Order SEIR Deterministic and Stochastic Models of Measles. Int. J. Environ. Res. Public Health 2020, 17, 2014. Islam, M.R.; Peace, A.; Medina, D.; Oraby, T. Integer Versus Fractional Order SEIR Deterministic and Stochastic Models of Measles. Int. J. Environ. Res. Public Health 2020, 17, 2014.

Journal reference: Int. J. Environ. Res. Public Health 2020, 17, 2014
DOI: 10.3390/ijerph17062014

Abstract

In this paper, we compare the performance between systems of ordinary and (Caputo) fractional differential equations depicting the susceptible-exposed-infectious-recovered (SEIR) models of diseases. In order to understand the origins of both approaches as mean-field approximations of integer and fractional stochastic processes, we introduce the fractional differential equations as approximations of some type of fractional nonlinear birth--death processes. Then, we examine validity of the two approaches against empirical courses of epidemics; we fit both of them to case counts of three measles epidemics that occurred during the pre-vaccination era in three different locations. While FDEs appear more flexible in fitting empirical data, our ODEs offered better fits to two out of three data sets. Important differences in transient dynamics between these modeling approaches are discussed.

Subject Areas

fractional SEIR stochastic model; Caputo fractional order differential equations; measles; parameter estimation

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