On the estimation of sequestered infected erythrocytes in Plasmodium falciparum malaria patients
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 exponen...
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| Format: | Article |
| Language: | English |
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AIMS Press
2014-02-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.741 |
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| author | Derdei Bichara Nathalie Cozic Abderrahman Iggidr |
| author_facet | Derdei Bichara Nathalie Cozic Abderrahman Iggidr |
| author_sort | Derdei Bichara |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-ee1ef316cc164148a6a9d355622fdd50 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2014-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-ee1ef316cc164148a6a9d355622fdd502025-01-24T02:28:18ZengAIMS PressMathematical Biosciences and Engineering1551-00182014-02-0111474175910.3934/mbe.2014.11.741On the estimation of sequestered infected erythrocytes in Plasmodium falciparum malaria patientsDerdei Bichara0Nathalie Cozic1Abderrahman Iggidr2Inria, Université de Lorraine, CNRS, Institut Elie Cartan de Lorraine, UMR 7502, ISGMP Bat. A, Metz, F-57045Inria, Université de Lorraine, CNRS, Institut Elie Cartan de Lorraine, UMR 7502, ISGMP Bat. A, Metz, F-57045Inria, Université de Lorraine, CNRS, Institut Elie Cartan de Lorraine, UMR 7502, ISGMP Bat. A, Metz, F-57045The 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.https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.741detectabilityage-structured modelsintra-host epidemic modelsobserversunknown inputs. |
| spellingShingle | Derdei Bichara Nathalie Cozic Abderrahman Iggidr On the estimation of sequestered infected erythrocytes in Plasmodium falciparum malaria patients Mathematical Biosciences and Engineering detectability age-structured models intra-host epidemic models observers unknown inputs. |
| title | On the estimation of sequestered infected erythrocytes in Plasmodium falciparum malaria patients |
| title_full | On the estimation of sequestered infected erythrocytes in Plasmodium falciparum malaria patients |
| title_fullStr | On the estimation of sequestered infected erythrocytes in Plasmodium falciparum malaria patients |
| title_full_unstemmed | On the estimation of sequestered infected erythrocytes in Plasmodium falciparum malaria patients |
| title_short | On the estimation of sequestered infected erythrocytes in Plasmodium falciparum malaria patients |
| title_sort | on the estimation of sequestered infected erythrocytes in plasmodium falciparum malaria patients |
| topic | detectability age-structured models intra-host epidemic models observers unknown inputs. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.741 |
| work_keys_str_mv | AT derdeibichara ontheestimationofsequesteredinfectederythrocytesinplasmodiumfalciparummalariapatients AT nathaliecozic ontheestimationofsequesteredinfectederythrocytesinplasmodiumfalciparummalariapatients AT abderrahmaniggidr ontheestimationofsequesteredinfectederythrocytesinplasmodiumfalciparummalariapatients |