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 <em> observer</em> or <em> estimator</em>, 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 <em> sequestered infected erythrocytes,</em> 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.
Highlights
Malaria is a disease that causes at least one million deaths around the world each year, with ninety per cent among African children. the most dangerous type of malaria is caused by the most virulent species of the Plasmodium parasite: Plasmodium falciparum
The estimation of sequestered parasite population has been a challenge for the biologist and modeler, with many authors [8, 7, 19] having studied this problem
We propose a different and simple method to estimate the total parasite concentration from the measured circulating parasites and we show how the parameter β can be estimated
Summary
Malaria is a disease that causes at least one million deaths around the world each year, with ninety per cent among African children. the most dangerous type of malaria is caused by the most virulent species of the Plasmodium parasite: Plasmodium falciparum. Parameters μx, μy and μm are the death rates of the uninfected erythrocytes, infected parasites and free merozoites respectively. At roughly the middle stage of trophozoite development (24 hours), molecules on the surface of infected erythrocytes link to receptors of endothelial cells. This bind has the effect of holding infected erythrocytes within vessels of organs (such as the brain), where they remain until the rupture of the erythrocyte and the release of merozoites. We propose a different and simple method to estimate the total parasite concentration from the measured circulating parasites and we show how the parameter β can be estimated To this end, we use some tools from control theory. The main idea here is to consider the infection term βxm as an unknown input and to use the theory of observers for systems with unknown inputs [10, 11] to provide the dynamical estimates
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