| Title:
|
Kermack-McKendrick epidemic model revisited (English) |
| Author:
|
Štěpán, Josef |
| Author:
|
Hlubinka, Daniel |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
43 |
| Issue:
|
4 |
| Year:
|
2007 |
| Pages:
|
395-414 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper proposes a stochastic diffusion model for the spread of a susceptible-infective-removed Kermack–McKendric epidemic (M1) in a population which size is a martingale $N_t$ that solves the Engelbert–Schmidt stochastic differential equation (). The model is given by the stochastic differential equation (M2) or equivalently by the ordinary differential equation (M3) whose coefficients depend on the size $N_t$. Theorems on a unique strong and weak existence of the solution to (M2) are proved and computer simulations performed. (English) |
| Keyword:
|
SIR epidemic models |
| Keyword:
|
stochastic differential equations |
| Keyword:
|
weak solution |
| Keyword:
|
simulation |
| MSC:
|
34F05 |
| MSC:
|
37N25 |
| MSC:
|
60H10 |
| MSC:
|
60H35 |
| MSC:
|
92D25 |
| idZBL:
|
Zbl 1137.37338 |
| idMR:
|
MR2377919 |
| . |
| Date available:
|
2009-09-24T20:24:56Z |
| Last updated:
|
2012-06-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135783 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| . |
