Mathematical Analysis of Malaria Epidemic: Asymptotic Stability With Cost-Effectiveness Study
Malaria is an old, curable vector-borne disease that is devastating in the tropics and subtropical regions of the world. The disease has unmatched complications in the human host, especially in children. Mathematical models of infectious diseases have been the steering wheel, driving scientists towa...
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| Format: | Article |
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Wiley
2024-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/5533885 |
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| author | Sacrifice Nana-Kyere Baba Seidu Kwara Nantomah |
| author_facet | Sacrifice Nana-Kyere Baba Seidu Kwara Nantomah |
| author_sort | Sacrifice Nana-Kyere |
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| description | Malaria is an old, curable vector-borne disease that is devastating in the tropics and subtropical regions of the world. The disease has unmatched complications in the human host, especially in children. Mathematical models of infectious diseases have been the steering wheel, driving scientists towards elucidation of the dynamic behaviour of epidemics and providing tailored strategic management of diseases. With the ongoing vaccination programs for vector-borne diseases, the research proposes a nonlinear differential equation model for the malaria disease that provides public health with a shift from the classical understanding of nonpharmaceutical preventive malaria control to pharmaceutical measures of vaccines. The asymptotic dynamic behaviour of the model is studied at the model’s equilibria. The bifurcation type invoked at the disease-free state is analysed, and the result revealed that the convention that R0<1 is the condition for eradicating the disease is not always sufficient when the system undergoes backward bifurcation. Furthermore, sensitivity analysis was investigated to quantify the amount of influence each parameter has on R0. With the Latin hypercube sampling and partial rank correlation coefficient method, the uncertainty in R0 is computed with a 95% confidence interval, with the mean, and 5th and 95th percentiles, respectively, simulated as 0.143788, 0.01545, and 0.41491. An intervention model was derived from the nonintervention model to experiment with and evaluate the respective effects of the various pairings of interventions on the dynamics of the disease. Lastly, an in-depth cost analysis was studied to identify the most cost-effective intervention regarding rewarding the desired outcome. From the analysis, we recommend that besides the nonpharmaceutical measure of bed nets and insecticide spray, public health should target the pharmaceutical intervention of vaccine as it can close the gap in malaria prevention. |
| format | Article |
| id | doaj-art-85c2aad162bd47c5bf43be432ae70c58 |
| institution | Kabale University |
| issn | 1687-0042 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-85c2aad162bd47c5bf43be432ae70c582025-02-03T07:23:26ZengWileyJournal of Applied Mathematics1687-00422024-01-01202410.1155/2024/5533885Mathematical Analysis of Malaria Epidemic: Asymptotic Stability With Cost-Effectiveness StudySacrifice Nana-Kyere0Baba Seidu1Kwara Nantomah2Department of MathematicsDepartment of MathematicsDepartment of MathematicsMalaria is an old, curable vector-borne disease that is devastating in the tropics and subtropical regions of the world. The disease has unmatched complications in the human host, especially in children. Mathematical models of infectious diseases have been the steering wheel, driving scientists towards elucidation of the dynamic behaviour of epidemics and providing tailored strategic management of diseases. With the ongoing vaccination programs for vector-borne diseases, the research proposes a nonlinear differential equation model for the malaria disease that provides public health with a shift from the classical understanding of nonpharmaceutical preventive malaria control to pharmaceutical measures of vaccines. The asymptotic dynamic behaviour of the model is studied at the model’s equilibria. The bifurcation type invoked at the disease-free state is analysed, and the result revealed that the convention that R0<1 is the condition for eradicating the disease is not always sufficient when the system undergoes backward bifurcation. Furthermore, sensitivity analysis was investigated to quantify the amount of influence each parameter has on R0. With the Latin hypercube sampling and partial rank correlation coefficient method, the uncertainty in R0 is computed with a 95% confidence interval, with the mean, and 5th and 95th percentiles, respectively, simulated as 0.143788, 0.01545, and 0.41491. An intervention model was derived from the nonintervention model to experiment with and evaluate the respective effects of the various pairings of interventions on the dynamics of the disease. Lastly, an in-depth cost analysis was studied to identify the most cost-effective intervention regarding rewarding the desired outcome. From the analysis, we recommend that besides the nonpharmaceutical measure of bed nets and insecticide spray, public health should target the pharmaceutical intervention of vaccine as it can close the gap in malaria prevention.http://dx.doi.org/10.1155/2024/5533885 |
| spellingShingle | Sacrifice Nana-Kyere Baba Seidu Kwara Nantomah Mathematical Analysis of Malaria Epidemic: Asymptotic Stability With Cost-Effectiveness Study Journal of Applied Mathematics |
| title | Mathematical Analysis of Malaria Epidemic: Asymptotic Stability With Cost-Effectiveness Study |
| title_full | Mathematical Analysis of Malaria Epidemic: Asymptotic Stability With Cost-Effectiveness Study |
| title_fullStr | Mathematical Analysis of Malaria Epidemic: Asymptotic Stability With Cost-Effectiveness Study |
| title_full_unstemmed | Mathematical Analysis of Malaria Epidemic: Asymptotic Stability With Cost-Effectiveness Study |
| title_short | Mathematical Analysis of Malaria Epidemic: Asymptotic Stability With Cost-Effectiveness Study |
| title_sort | mathematical analysis of malaria epidemic asymptotic stability with cost effectiveness study |
| url | http://dx.doi.org/10.1155/2024/5533885 |
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