Mathematical modeling of the effects of public health education on tungiasis—a neglected disease with many challenges in endemic communities
Abstract In this paper, we formulate and study a mathematical model for the dynamics of jigger infestation incorporating public health education using systems of ordinary differential equations and computational simulations. The basic reproduction number RE $R_{E}$ is obtained and used to determine...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-11-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-018-1875-5 |
| _version_ | 1818361347563323392 |
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| author | Rachel A. Nyang’inja David N. Angwenyi Cecilia M. Musyoka Titus O. Orwa |
| author_facet | Rachel A. Nyang’inja David N. Angwenyi Cecilia M. Musyoka Titus O. Orwa |
| author_sort | Rachel A. Nyang’inja |
| collection | DOAJ |
| description | Abstract In this paper, we formulate and study a mathematical model for the dynamics of jigger infestation incorporating public health education using systems of ordinary differential equations and computational simulations. The basic reproduction number RE $R_{E}$ is obtained and used to determine whether the disease breaks out in the population and results in an endemic equilibrium or dies out eventually corresponding to a disease-free equilibrium. We carried out an analysis of the model and established the conditions for the local and global stabilities of the disease-free and endemic equilibria points. Using the Lyapunov stability theory and LaSalle invariant principle, we found out that the disease-endemic equilibrium point is globally asymptotically stable if RE>1 $R_{E}>1$ and unstable otherwise. Numerical simulations are performed to illustrate our theoretical predictions. Both the analytical and numerical results show public health education is a very effective control measure in eradicating jigger infestation in the endemic communities at large. |
| first_indexed | 2024-12-13T21:15:15Z |
| format | Article |
| id | doaj.art-339f92c7097444b0a3d1675e5541ca2d |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-13T21:15:15Z |
| publishDate | 2018-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-339f92c7097444b0a3d1675e5541ca2d2022-12-21T23:31:15ZengSpringerOpenAdvances in Difference Equations1687-18472018-11-012018111910.1186/s13662-018-1875-5Mathematical modeling of the effects of public health education on tungiasis—a neglected disease with many challenges in endemic communitiesRachel A. Nyang’inja0David N. Angwenyi1Cecilia M. Musyoka2Titus O. Orwa3Department of Mathematics, Shanghai UniversityDepartment of Mathematics, Masinde Muliro University of Science and TechnologyDepartment of Mathematics, Shanghai UniversityInstitute of Mathematical Sciences, Strathmore UniversityAbstract In this paper, we formulate and study a mathematical model for the dynamics of jigger infestation incorporating public health education using systems of ordinary differential equations and computational simulations. The basic reproduction number RE $R_{E}$ is obtained and used to determine whether the disease breaks out in the population and results in an endemic equilibrium or dies out eventually corresponding to a disease-free equilibrium. We carried out an analysis of the model and established the conditions for the local and global stabilities of the disease-free and endemic equilibria points. Using the Lyapunov stability theory and LaSalle invariant principle, we found out that the disease-endemic equilibrium point is globally asymptotically stable if RE>1 $R_{E}>1$ and unstable otherwise. Numerical simulations are performed to illustrate our theoretical predictions. Both the analytical and numerical results show public health education is a very effective control measure in eradicating jigger infestation in the endemic communities at large.http://link.springer.com/article/10.1186/s13662-018-1875-5Basic reproduction numberGlobal stabilityJigger infestationLyapunov stability theoryPublic health education |
| spellingShingle | Rachel A. Nyang’inja David N. Angwenyi Cecilia M. Musyoka Titus O. Orwa Mathematical modeling of the effects of public health education on tungiasis—a neglected disease with many challenges in endemic communities Advances in Difference Equations Basic reproduction number Global stability Jigger infestation Lyapunov stability theory Public health education |
| title | Mathematical modeling of the effects of public health education on tungiasis—a neglected disease with many challenges in endemic communities |
| title_full | Mathematical modeling of the effects of public health education on tungiasis—a neglected disease with many challenges in endemic communities |
| title_fullStr | Mathematical modeling of the effects of public health education on tungiasis—a neglected disease with many challenges in endemic communities |
| title_full_unstemmed | Mathematical modeling of the effects of public health education on tungiasis—a neglected disease with many challenges in endemic communities |
| title_short | Mathematical modeling of the effects of public health education on tungiasis—a neglected disease with many challenges in endemic communities |
| title_sort | mathematical modeling of the effects of public health education on tungiasis a neglected disease with many challenges in endemic communities |
| topic | Basic reproduction number Global stability Jigger infestation Lyapunov stability theory Public health education |
| url | http://link.springer.com/article/10.1186/s13662-018-1875-5 |
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