2021 Optimal Control in Two Strain Pneumonia Transmission Dynamics
Mary C. Swai, Nyimvua Shaban, Theresia Marijani
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J. Appl. Math. 2021: 1-21 (2021). DOI: 10.1155/2021/8835918


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.


M. Swai is grateful for the support provided by the Open University of Tanzania.


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Mary C. Swai. Nyimvua Shaban. Theresia Marijani. "Optimal Control in Two Strain Pneumonia Transmission Dynamics." J. Appl. Math. 2021 1 - 21, 2021. https://doi.org/10.1155/2021/8835918


Received: 25 September 2020; Revised: 15 December 2020; Accepted: 4 January 2021; Published: 2021
First available in Project Euclid: 28 July 2021

Digital Object Identifier: 10.1155/2021/8835918

Rights: Copyright © 2021 Hindawi


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