Applications of Mathematics, Vol. 63, No. 3, pp. 259-271, 2018


Reliable numerical modelling of malaria propagation

István Faragó, Miklós Emil Mincsovics, Rahele Mosleh

Received April 3, 2018.   Published online June 25, 2018.

Abstract:  We investigate biological processes, particularly the propagation of malaria. Both the continuous and the numerical models on some fixed mesh should preserve the basic qualitative properties of the original phenomenon. Our main goal is to give the conditions for the discrete (numerical) models of the malaria phenomena under which they possess some given qualitative property, namely, to be between zero and one. The conditions which guarantee this requirement are related to the time-discretization step-size. We give a sufficient condition for some explicit methods. For implicit methods we prove that the above property holds unconditionally.
Keywords:  epidemic model; qualitative propertie; non-negativity; finite difference method
Classification MSC:  65M06, 35Q92, 34C60


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Affiliations:   István Faragó, Department of Applied Analysis and Computational Mathematics, Faculty of Science, Eötvös Loránd University, 1117, Budapest Pazmany P. s. 1/C., Hungary; MTA-ELTE Research Group, 1117, Budapest Pazmany P. s. 1/C., Hungary; Department of Differential Equations, Budapest University of Technology and Economics, 1111 Budapest Egry József str. 1, Hungary, e-mail: faragois@cs.elte.hu; Miklós Emil Mincsovics, MTA-ELTE Research Group, 1117, Budapest Pazmany P. s. 1/C., Hungary; Department of Differential Equations, Budapest University of Technology and Economics, 1111 Budapest Egry József str. 1, Hungary, e-mail: mincso@cs.elte.hu; Rahele Mosleh, Department of Differential Equations, Budapest University of Technology and Economics, 1111 Budapest Egry József str. 1, Hungary, e-mail: rmosleh028@gmail.com


 
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