| Title:
|
Reliable numerical modelling of malaria propagation (English) |
| Author:
|
Faragó, István |
| Author:
|
Mincsovics, Miklós Emil |
| Author:
|
Mosleh, Rahele |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
63 |
| Issue:
|
3 |
| Year:
|
2018 |
| Pages:
|
259-271 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
epidemic model |
| Keyword:
|
qualitative propertie |
| Keyword:
|
non-negativity |
| Keyword:
|
finite difference method |
| MSC:
|
34C60 |
| MSC:
|
35Q92 |
| MSC:
|
65L06 |
| MSC:
|
65M06 |
| MSC:
|
92D30 |
| idZBL:
|
Zbl 06945732 |
| idMR:
|
MR3833660 |
| DOI:
|
10.21136/AM.2018.0098-18 |
| . |
| Date available:
|
2018-07-16T08:48:07Z |
| Last updated:
|
2020-07-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147310 |
| . |
| Reference:
|
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| Reference:
|
[2] Capasso, V.: Mathematical Structures of Epidemic Systems.Lecture Notes in Biomathematics 97, Springer, Berlin (2008). Zbl 1141.92035, MR 2722340, 10.1007/978-3-540-70514-7 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
[10] Ruan, S., Xiao, D., Beier, J. C.: On the delayed Ross-Macdonald model for malaria transmission.Bull. Math. Biol. 70 (2008), 1098-1114. Zbl 1142.92040, MR 2391181, 10.1007/s11538-007-9292-z |
| Reference:
|
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| Reference:
|
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| . |
