On a fractional order Ebola epidemic model

Abstract

Ebola is a world health problem and with a recent outbreak. There exist different models in the literature to predict its behavior, most of them based on data coming from previous outbreaks or using restricted number of persons in the population variable. This paper deals both with classical and fractional order SEIR (susceptible, exposed, infections, removed) Ebola epidemic model and its comparison with real data extracted from the reports periodically published by the World Health Organization (WHO), starting from March 27th, 2014. As it has been shown in the literature, one physical meaning of the fractional order in fractional derivatives is that of index of memory; and therefore, it seems to be useful for epidemic models, as in this paper. The number of confirmed cases by the WHO in its reports is used for our analysis and estimation of the parameters in our classical and fractional SEIR models. Our approach gives a good approximation to real data. Following our results, the current outbreak will continue for approximately two years, assuming that no new outbreak appears at a different community or country. Our estimates give a number of the order nine million confirmed cases. MSC: Primary 26A33; secondary 34A08

Dynamics and Optimal Control of Ebola Transmission

“…1 Compartment diagram of the Susceptible-Exposed-Infectious-Recovered (SEIR) model (2) Transitions between different states are described by the following parameters:…”

Analysis, simulation and optimal control of a seir model for ebola virus with demographic effects

“…In this section, we study a model with vital dynamics by considering the birth and death rates. Such model is new in the Ebola context [2,26,27,28,29,30,38].…”

“…The basic reproduction ratio R 0 is given by the dominant eigenvalue of the matrix F V 1 [17]. Applying the next generation method to the SEIR model (2), and since we are only concerned with individuals that spread the infection, we only need to model the exposed, E, and infected, I, classes. Let us de…ne the model dynamics using the equations 8 > > < > > :…”

An Analysis on the Fractional Asset Flow Differential Equations

“…The most regular definition is the Liouville-Caputo-type definition because the initial condition for fractional order differential equations with Liouville-Caputo-type derivatives is similar in form to the integer-order differential equation [19][20][21][22]. Lemma 1.…”

“…The traditional system of integer-order of differential equations may fail to explain complicated incidents in real phenomena. However, nowadays, fractional order of differential equations has been applied to model the complicated real situations involving many areas-for example, physics, engineering, epidemic, finance and sciences [19][20][21][22][23][24]. The concept of a fractional model helps with expressing the data structure for real life situations more than the integer model.…”