On the estimation of sequestered infected erythrocytes in <em>Plasmodium falciparum</em> malaria patients

International audienceThe 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