# American Institute of Mathematical Sciences

2014, 11(4): 741-759. doi: 10.3934/mbe.2014.11.741

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

 1 Inria, Université de Lorraine, CNRS, Institut Elie Cartan de Lorraine, UMR 7502, ISGMP Bat. A, Metz, F-57045, France, France, France

Received  January 2013 Revised  December 2013 Published  March 2014

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 observer or 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 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.
Citation: Derdei Bichara, Nathalie Cozic, Abderrahman Iggidr. On the estimation of sequestered infected erythrocytes in Plasmodium falciparum malaria patients. Mathematical Biosciences & Engineering, 2014, 11 (4) : 741-759. doi: 10.3934/mbe.2014.11.741
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