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Article

Integer Versus Fractional Order SEIR Deterministic and Stochastic Models of Measles

1
Department of Mathematics and Statistics, Texas Tech University, 2500 Broadway, Lubbock, TX 79409, USA
2
School of Mathematical and Statistical Sciences, The University of Texas Rio Grande Valley, 1201 W. University Drive, Edinburg, TX 78539, USA
*
Author to whom correspondence should be addressed.
Int. J. Environ. Res. Public Health 2020, 17(6), 2014; https://doi.org/10.3390/ijerph17062014
Received: 25 January 2020 / Revised: 6 March 2020 / Accepted: 9 March 2020 / Published: 18 March 2020
(This article belongs to the Special Issue Infectious Disease Modeling in the Era of Complex Data)
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 (FDEs) as approximations of some type of fractional nonlinear birth and 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 ordinary differential equations (ODEs) are commonly used to model epidemics, FDEs are more flexible in fitting empirical data and theoretically offer improved model predictions. The question arises whether, in practice, the benefits of using FDEs over ODEs outweigh the added computational complexities. While important differences in transient dynamics were observed, the FDE only outperformed the ODE in one of out three data sets. In general, FDE modeling approaches may be worth it in situations with large refined data sets and good numerical algorithms. View Full-Text
Keywords: fractional SEIR stochastic model; caputo fractional order differential equations; measles; parameter estimation fractional SEIR stochastic model; caputo fractional order differential equations; measles; parameter estimation
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MDPI and ACS Style

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. https://doi.org/10.3390/ijerph17062014

AMA Style

Islam MR, Peace A, Medina D, Oraby T. Integer Versus Fractional Order SEIR Deterministic and Stochastic Models of Measles. International Journal of Environmental Research and Public Health. 2020; 17(6):2014. https://doi.org/10.3390/ijerph17062014

Chicago/Turabian Style

Islam, Md R., Angela Peace, Daniel Medina, and Tamer Oraby. 2020. "Integer Versus Fractional Order SEIR Deterministic and Stochastic Models of Measles" International Journal of Environmental Research and Public Health 17, no. 6: 2014. https://doi.org/10.3390/ijerph17062014

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