Optimal Control in Two Strain Pneumonia Transmission Dynamics
A mathematical model for the transmission dynamics of pneumonia disease in the presence of drug resistance is formulated. Intervention strategies, namely, vaccination, public health education, and treatment are implemented. We compute the effective reproduction numbers and establish the local stabil...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/8835918 |
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| author | Mary C. Swai Nyimvua Shaban Theresia Marijani |
| author_facet | Mary C. Swai Nyimvua Shaban Theresia Marijani |
| author_sort | Mary C. Swai |
| collection | DOAJ |
| description | A mathematical model for the transmission dynamics of pneumonia disease in the presence of drug resistance is formulated. Intervention strategies, namely, vaccination, public health education, and treatment are implemented. We compute the effective reproduction numbers and establish the local stability of the equilibria of the model. Global stability of the disease-free equilibrium is obtained through the comparison method. On the other hand, we apply the Lyapunov method to show that the drug-resistant equilibrium is globally asymptotically stable under some feasible biological conditions. Furthermore, we apply optimal control theory to the model aiming at minimizing the number of infections from drug-sensitive and drug-resistant strains. The necessary conditions for the optimal solutions of the model were derived by using Pontryagin’s Maximum Principle. The optimal controls are characterized in terms of the optimality system, which is solved numerically for several scenarios to investigate the best strategy. The incremental cost-effectiveness analysis technique is used to find the most cost-effective strategy, and it is observed that the vaccination program is the most cost-effective strategy in case of limited resources. However, results show that implementing the three strategies simultaneously provides the best results in controlling the disease. |
| format | Article |
| id | doaj-art-9c110bcf09454245acd695d7391f66ae |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-9c110bcf09454245acd695d7391f66ae2025-02-03T01:25:25ZengWileyJournal of Applied Mathematics1110-757X1687-00422021-01-01202110.1155/2021/88359188835918Optimal Control in Two Strain Pneumonia Transmission DynamicsMary C. Swai0Nyimvua Shaban1Theresia Marijani2Department of Mathematics, University of Dar-es-Salaam, P.O. Box 35062, Dar-es-Salaam, TanzaniaDepartment of Mathematics, University of Dar-es-Salaam, P.O. Box 35062, Dar-es-Salaam, TanzaniaDepartment of Mathematics, University of Dar-es-Salaam, P.O. Box 35062, Dar-es-Salaam, TanzaniaA mathematical model for the transmission dynamics of pneumonia disease in the presence of drug resistance is formulated. Intervention strategies, namely, vaccination, public health education, and treatment are implemented. We compute the effective reproduction numbers and establish the local stability of the equilibria of the model. Global stability of the disease-free equilibrium is obtained through the comparison method. On the other hand, we apply the Lyapunov method to show that the drug-resistant equilibrium is globally asymptotically stable under some feasible biological conditions. Furthermore, we apply optimal control theory to the model aiming at minimizing the number of infections from drug-sensitive and drug-resistant strains. The necessary conditions for the optimal solutions of the model were derived by using Pontryagin’s Maximum Principle. The optimal controls are characterized in terms of the optimality system, which is solved numerically for several scenarios to investigate the best strategy. The incremental cost-effectiveness analysis technique is used to find the most cost-effective strategy, and it is observed that the vaccination program is the most cost-effective strategy in case of limited resources. However, results show that implementing the three strategies simultaneously provides the best results in controlling the disease.http://dx.doi.org/10.1155/2021/8835918 |
| spellingShingle | Mary C. Swai Nyimvua Shaban Theresia Marijani Optimal Control in Two Strain Pneumonia Transmission Dynamics Journal of Applied Mathematics |
| title | Optimal Control in Two Strain Pneumonia Transmission Dynamics |
| title_full | Optimal Control in Two Strain Pneumonia Transmission Dynamics |
| title_fullStr | Optimal Control in Two Strain Pneumonia Transmission Dynamics |
| title_full_unstemmed | Optimal Control in Two Strain Pneumonia Transmission Dynamics |
| title_short | Optimal Control in Two Strain Pneumonia Transmission Dynamics |
| title_sort | optimal control in two strain pneumonia transmission dynamics |
| url | http://dx.doi.org/10.1155/2021/8835918 |
| work_keys_str_mv | AT marycswai optimalcontrolintwostrainpneumoniatransmissiondynamics AT nyimvuashaban optimalcontrolintwostrainpneumoniatransmissiondynamics AT theresiamarijani optimalcontrolintwostrainpneumoniatransmissiondynamics |