On the estimation of sequestered infected erythrocytes in Plasmodium falciparum malaria patients

Derdei Bichara 1, 2 Nathalie Cozic 1, 2 Abderrahman Iggidr 2, 1, *
* Auteur correspondant
1 MASAIE - Tools and models of nonlinear control theory for epidemiology and immunology
LMAM - Laboratoire de Mathématiques et Applications de Metz, Inria Nancy - Grand Est, IECL - Institut Élie Cartan de Lorraine
2 EDP - Equations aux dérivées partielles
IECL - Institut Élie Cartan de Lorraine
Abstract : The aim of this paper is to give a method for the estimation of total parasite burden of the patient and the rate of infection in a malaria's intra-host model by using control theory tools. More precisely, we use an auxiliary system, called {\it observer} or {\it estimator}, whose solutions tend exponentially to those of the original model. This observer uses only the available measurable data, namely, the values of peripheral infected erythrocytes. It provides estimates of the {\it sequestered infected erythrocytes,} that cannot be measured by clinical methods. Therefore this method allows to estimate the total parasite burden within a malaria patient. Moreover, our constructed observer does not use the uncertain infection rate parameter $\beta$. In fact, we derive a simple method to estimate this parameter $\beta$. We apply this estimation method using real data that have been collected when malaria was used as therapy for neurosyphilis by the US Public Health Service.
Type de document :
Article dans une revue
Mathematical Biosciences and Engineering (MBE), American Institute of Mathematical Sciences, 2014, 11 (4), pp.741 - 759. 〈http://aimsciences.org/journals/pdfs.jsp?paperID=9736&mode=full〉. 〈10.3934/mbe.2014.11.741〉
Liste complète des métadonnées

Littérature citée [21 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/hal-00922456
Contributeur : Abderrahman Iggidr <>
Soumis le : jeudi 26 décembre 2013 - 20:42:31
Dernière modification le : jeudi 11 janvier 2018 - 06:26:21
Document(s) archivé(s) le : vendredi 28 mars 2014 - 17:02:58

Fichier

MBE0317authorversion.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Derdei Bichara, Nathalie Cozic, Abderrahman Iggidr. On the estimation of sequestered infected erythrocytes in Plasmodium falciparum malaria patients. Mathematical Biosciences and Engineering (MBE), American Institute of Mathematical Sciences, 2014, 11 (4), pp.741 - 759. 〈http://aimsciences.org/journals/pdfs.jsp?paperID=9736&mode=full〉. 〈10.3934/mbe.2014.11.741〉. 〈hal-00922456〉

Partager

Métriques

Consultations de la notice

631

Téléchargements de fichiers

228