Reliable numerical modelling of malaria propagation

István Faragó; Miklós Emil Mincsovics; Rahele Mosleh

Applications of Mathematics (2018)

  • Volume: 63, Issue: 3, page 259-271
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Faragó, István, Mincsovics, Miklós Emil, and Mosleh, Rahele. "Reliable numerical modelling of malaria propagation." Applications of Mathematics 63.3 (2018): 259-271. <http://eudml.org/doc/294369>.

@article{Faragó2018,
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.},
author = {Faragó, István, Mincsovics, Miklós Emil, Mosleh, Rahele},
journal = {Applications of Mathematics},
keywords = {epidemic model; qualitative propertie; non-negativity; finite difference method},
language = {eng},
number = {3},
pages = {259-271},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Reliable numerical modelling of malaria propagation},
url = {http://eudml.org/doc/294369},
volume = {63},
year = {2018},
}

TY - JOUR
AU - Faragó, István
AU - Mincsovics, Miklós Emil
AU - Mosleh, Rahele
TI - Reliable numerical modelling of malaria propagation
JO - Applications of Mathematics
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 3
SP - 259
EP - 271
AB - 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.
LA - eng
KW - epidemic model; qualitative propertie; non-negativity; finite difference method
UR - http://eudml.org/doc/294369
ER -

References

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  7. Kermack, W. O., McKendrick, A. G., 10.1098/rspa.1927.0118, Proc. R. Soc. Lond., Ser. A 115 (1927), 700-721. (1927) Zbl53.0517.01DOI10.1098/rspa.1927.0118
  8. Mandal, S., Sarkar, R. R., Sinha, S., 10.1186/1475-2875-10-202, Malaria Journal 10 (2011). (2011) MR2756727DOI10.1186/1475-2875-10-202
  9. Ross, R., The Prevention of Malaria, John Murray, London (1911). (1911) 
  10. Ruan, S., Xiao, D., Beier, J. C., 10.1007/s11538-007-9292-z, Bull. Math. Biol. 70 (2008), 1098-1114. (2008) Zbl1142.92040MR2391181DOI10.1007/s11538-007-9292-z
  11. Smith, H., 10.1007/978-1-4419-7646-8, Texts in Applied Mathematics 57, Springer, New York (2011). (2011) Zbl1227.34001MR2724792DOI10.1007/978-1-4419-7646-8
  12. WHO.malaria, Available at: http://www.who.int/en/news-room/fact-sheets/de-tail/malaria, . 

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