Optimal control for co-infection with COVID-19-Associated Pulmonary Aspergillosis in ICU patients with environmental contamination

Nandhini Mohankumar; Lavanya Rajagopal; Juan J. Nieto; Nandhini Mohankumar; Lavanya Rajagopal; Juan J. Nieto

doi:10.3934/mbe.2023432

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 6: 9861-9875. doi: 10.3934/mbe.2023432

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Research article

Optimal control for co-infection with COVID-19-Associated Pulmonary Aspergillosis in ICU patients with environmental contamination

1.
Department of Mathematics, Coimbatore Institute of Technology, Tamilnadu, India
2.
CITMAga, Departamento de Estatística, Análise Matemática e Optimización, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain

Received: 25 January 2023 Revised: 06 March 2023 Accepted: 12 March 2023 Published: 24 March 2023

In this paper, we propose a mathematical model for COVID-19-Associated Pulmonary Aspergillosis (CAPA) co-infection, that enables the study of relationship between prevention and treatment. The next generation matrix is employed to find the reproduction number. We enhanced the co-infection model by incorporating time-dependent controls as interventions based on Pontryagin's maximum principle in obtaining the necessary conditions for optimal control. Finally, we perform numerical experiments with different control groups to assess the elimination of infection. In numerical results, transmission prevention control, treatment controls, and environmental disinfection control provide the best chance of preventing the spread of diseases more rapidly than any other combination of controls.
- co-infection,
- CAPA,
- hospital environment,
- reproduction number,
- optimal control
Citation: Nandhini Mohankumar, Lavanya Rajagopal, Juan J. Nieto. Optimal control for co-infection with COVID-19-Associated Pulmonary Aspergillosis in ICU patients with environmental contamination[J]. Mathematical Biosciences and Engineering, 2023, 20(6): 9861-9875. doi: 10.3934/mbe.2023432

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Abstract

In this paper, we propose a mathematical model for COVID-19-Associated Pulmonary Aspergillosis (CAPA) co-infection, that enables the study of relationship between prevention and treatment. The next generation matrix is employed to find the reproduction number. We enhanced the co-infection model by incorporating time-dependent controls as interventions based on Pontryagin's maximum principle in obtaining the necessary conditions for optimal control. Finally, we perform numerical experiments with different control groups to assess the elimination of infection. In numerical results, transmission prevention control, treatment controls, and environmental disinfection control provide the best chance of preventing the spread of diseases more rapidly than any other combination of controls.

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