Continuous and pulsed epidemiological models for onchocerciasis with implications for eradication strategy
Onchocerciasis is an endemic disease in parts of sub-Saharan Africa. Complex mathematical models are being used to assess the likely efficacy of efforts to eradicate the disease; however, their predictions have not always been borne out in practice. In this paper, we represent the immunological aspe...
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AIMS Press
2018-07-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2018038 |
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| author | Glenn Ledder Donna Sylvester Rachelle R. Bouchat Johann A. Thiel |
| author_facet | Glenn Ledder Donna Sylvester Rachelle R. Bouchat Johann A. Thiel |
| author_sort | Glenn Ledder |
| collection | DOAJ |
| description | Onchocerciasis is an endemic disease in parts of sub-Saharan Africa. Complex mathematical models are being used to assess the likely efficacy of efforts to eradicate the disease; however, their predictions have not always been borne out in practice. In this paper, we represent the immunological aspects of the disease with a single empirical parameter in order to reduce the model complexity. Asymptotic approximation allows us to reduce the vector-borne epidemiological model to a model of an infectious disease with nonlinear incidence. We then consider two versions, one with continuous treatment and a more realistic one where treatment occurs only at intervals. Thorough mathematical analysis of these models yields equilibrium solutions for the continuous case, periodic solutions for the pulsed case, and conditions for the existence of endemic disease equilibria in both cases, thereby leading to simple model criteria for eradication. The analytical results and numerical experiments show that the continuous treatment version is an excellent approximation for the pulsed version and that the current onchocerciasis eradication strategy is inadequate for regions where the incidence is highest and unacceptably slow even when the long-term behavior is the disease-free state. |
| format | Article |
| id | doaj-art-c8a16756f6dc41d293748b10c109b68d |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2018-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-c8a16756f6dc41d293748b10c109b68d2025-01-24T02:40:56ZengAIMS PressMathematical Biosciences and Engineering1551-00182018-07-0115484186210.3934/mbe.2018038Continuous and pulsed epidemiological models for onchocerciasis with implications for eradication strategyGlenn Ledder0Donna Sylvester1Rachelle R. Bouchat2Johann A. Thiel3Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588-0130, USAMathematics Department, Seattle University, 901 12th Ave, Seattle, WA 98122-1090, USADepartment of Mathematics, Indiana University of Pennsylvania, Indiana, PA 15705, USADepartment of Mathematics, New York City College of Technology -CUNY, Brooklyn, NY 11201, USAOnchocerciasis is an endemic disease in parts of sub-Saharan Africa. Complex mathematical models are being used to assess the likely efficacy of efforts to eradicate the disease; however, their predictions have not always been borne out in practice. In this paper, we represent the immunological aspects of the disease with a single empirical parameter in order to reduce the model complexity. Asymptotic approximation allows us to reduce the vector-borne epidemiological model to a model of an infectious disease with nonlinear incidence. We then consider two versions, one with continuous treatment and a more realistic one where treatment occurs only at intervals. Thorough mathematical analysis of these models yields equilibrium solutions for the continuous case, periodic solutions for the pulsed case, and conditions for the existence of endemic disease equilibria in both cases, thereby leading to simple model criteria for eradication. The analytical results and numerical experiments show that the continuous treatment version is an excellent approximation for the pulsed version and that the current onchocerciasis eradication strategy is inadequate for regions where the incidence is highest and unacceptably slow even when the long-term behavior is the disease-free state.https://www.aimspress.com/article/doi/10.3934/mbe.2018038epidemiologydynamical modelsasymptotics |
| spellingShingle | Glenn Ledder Donna Sylvester Rachelle R. Bouchat Johann A. Thiel Continuous and pulsed epidemiological models for onchocerciasis with implications for eradication strategy Mathematical Biosciences and Engineering epidemiology dynamical models asymptotics |
| title | Continuous and pulsed epidemiological models for onchocerciasis with implications for eradication strategy |
| title_full | Continuous and pulsed epidemiological models for onchocerciasis with implications for eradication strategy |
| title_fullStr | Continuous and pulsed epidemiological models for onchocerciasis with implications for eradication strategy |
| title_full_unstemmed | Continuous and pulsed epidemiological models for onchocerciasis with implications for eradication strategy |
| title_short | Continuous and pulsed epidemiological models for onchocerciasis with implications for eradication strategy |
| title_sort | continuous and pulsed epidemiological models for onchocerciasis with implications for eradication strategy |
| topic | epidemiology dynamical models asymptotics |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2018038 |
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