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Global analysis of marchuk's model in a case of weak immune system

✍ Scribed by U. Forys

Book ID
104351533
Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
660 KB
Volume
25
Category
Article
ISSN
0895-7177

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✦ Synopsis

some special cases of Marchuk's simplest model of an infectious disease are considered.

We assume that damage to the target organ is not too large so a paralysis effect is neglected and the model reduces to three ordinary differential equations with time delay. The initial condition corresponds to a healthy organism infected by some dose of an antigen at time 0.

It is proved that if the immune system is weak and the antigen reproduction rate is large, then the end of every infection is lethal. This means that the antigen concentration increases to infinity in time.

The same is true if the antigen reproduction rate is small but the initial dose of antigen is sufficiently large.

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