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Optimal control of infectious disease: Information-induced vaccination and limited treatment

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  • Kumar, Anuj
  • Srivastava, Prashant K.
  • Dong, Yueping
  • Takeuchi, Yasuhiro

Abstract

In this study, a nonlinear compartmental model for an infectious disease is proposed. The spread of information is considered due to spread of disease in the population. The dynamics of the information is modeled by a separate rate equation and it is assumed that the growth of the information depends on the density of the infective population. The model accounts for the effect of information on vaccination coverage during the epidemic outbreak when medical resources for treatment are limited. Further, considering information-induced vaccination and treatment as controls, an optimal control problem is proposed which minimizes costs incurred due to the disease burden and applied controls. The total incurred cost is determined by taking a weighted sum of cost of productivity loss due to disease and costs incurred in applying control interventions. A higher nonlinearity in cost is considered for information induced vaccination efforts. With the help of Pontryagin’s Maximum Principle, the control system is analyzed and optimal control profiles for the applied controls are obtained. We further numerically explore the optimal control problem. A comparative study is made by choosing following control strategies: (A) execution of only information-induced vaccination, (B) implementation of only treatment and (C) execution of both the policies simultaneously. We observe that the comprehensive use of control interventions reduces the severity of the disease burden and also minimizes the economic burden incurred due to these interventions. Further, the effect of the basic reproduction number on the proposed control strategies as well as on the dynamics of infectious diseases is investigated. The numerical results infer that the treatment is more effective and economically feasible for a mild epidemic, while the information induced vaccination is more efficient for a serious epidemic.

Suggested Citation

  • Kumar, Anuj & Srivastava, Prashant K. & Dong, Yueping & Takeuchi, Yasuhiro, 2020. "Optimal control of infectious disease: Information-induced vaccination and limited treatment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    • Handle: RePEc:eee:phsmap:v:542:y:2020:i:c:s0378437119317972
    DOI: 10.1016/j.physa.2019.123196
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    References listed on IDEAS

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    1. Christina E. Mills & James M. Robins & Marc Lipsitch, 2004. "Transmissibility of 1918 pandemic influenza," Nature, Nature, vol. 432(7019), pages 904-906, December.
    2. Goldman Steven Marc & Lightwood James, 2002. "Cost Optimization in the SIS Model of Infectious Disease with Treatment," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 2(1), pages 1-24, April.
    3. Mark Gersovitz & Jeffrey S. Hammer, 2004. "The Economical Control of Infectious Diseases," Economic Journal, Royal Economic Society, vol. 114(492), pages 1-27, January.
    4. Kumar, Anuj & Srivastava, Prashant K. & Gupta, R.P., 2019. "Nonlinear dynamics of infectious diseases via information-induced vaccination and saturated treatment," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 157(C), pages 77-99.
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    Cited by:

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    2. Svetlana Kolesnikova & Ekaterina Kustova, 2023. "Application of a Stochastic Extension of the Analytical Design of Aggregated Regulators to a Multidimensional Biomedical Object," Mathematics, MDPI, vol. 11(21), pages 1-20, October.
    3. Kumar, Arjun & Dubey, Uma S. & Dubey, Balram, 2024. "The impact of social media advertisements and treatments on the dynamics of infectious diseases with optimal control strategies," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 50-86.
    4. Chao Liu & Peng Chen & Qiyu Jia & Lora Cheung, 2022. "Effects of Media Coverage on Global Stability Analysis and Optimal Control of an Age-Structured Epidemic Model with Multi-Staged Progression," Mathematics, MDPI, vol. 10(15), pages 1-28, August.
    5. Xu, Yuan-Hao & Wang, Hao-Jie & Lu, Zhong-Wen & Hu, Mao-Bin, 2023. "Impact of awareness dissemination on epidemic reaction–diffusion in multiplex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 621(C).
    6. Bing Li & Ziye Xiang, 2023. "Evolutionary Game of Vaccination Considering Both Epidemic and Economic Factors by Infectious Network of Complex Nodes," Mathematics, MDPI, vol. 11(12), pages 1-26, June.
    7. Aldila, Dipo, 2020. "Analyzing the impact of the media campaign and rapid testing for COVID-19 as an optimal control problem in East Java, Indonesia," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).

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