Dynamic analysis and optimal control of co-infection system under different outbreak times of mutant strains

Bolin Zhu; Dong Qiu; Bolin Zhu; Dong Qiu

doi:10.3934/Allergy.2024009

AIMS Allergy and Immunology

2024, Volume 8, Issue 3: 167-192. doi: 10.3934/Allergy.2024009

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Research article

Dynamic analysis and optimal control of co-infection system under different outbreak times of mutant strains

Bolin Zhu ,
Dong Qiu ^,

College of Science, Chongqing University of Posts and Telecommunications, Nanan, Chongqing, 400065, China

Received: 16 May 2024 Revised: 01 September 2024 Accepted: 19 September 2024 Published: 29 September 2024

In epidemic prevention efforts, the emergence of new virus strains due to mutations greatly complicates the prediction and management of epidemics. Most of the current mathematical models of infectious diseases assume that the mutant strain and the original strain have the same outbreak time, which is obviously an ideal situation. In order to make the study more practical, we consider the general situation of outbreaks of mutated strains. At the same time, the optimal control strategy under different emergence time of mutant strains was proposed by using the optimal control theory and numerical simulation. This study provides a new theoretical framework for the dual strain competition model with different outbreak times. The final theoretical results and numerical simulation showed that although the emergence time of the mutant did not affect the final trend of the epidemic, it would affect the cost of prevention and control during the control period.
- virus mutation models,
- Lyapunov equation,
- basic reproduction number,
- optimal control,
- Pontryagin's maximum principle
Citation: Bolin Zhu, Dong Qiu. Dynamic analysis and optimal control of co-infection system under different outbreak times of mutant strains[J]. AIMS Allergy and Immunology, 2024, 8(3): 167-192. doi: 10.3934/Allergy.2024009

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Abstract

In epidemic prevention efforts, the emergence of new virus strains due to mutations greatly complicates the prediction and management of epidemics. Most of the current mathematical models of infectious diseases assume that the mutant strain and the original strain have the same outbreak time, which is obviously an ideal situation. In order to make the study more practical, we consider the general situation of outbreaks of mutated strains. At the same time, the optimal control strategy under different emergence time of mutant strains was proposed by using the optimal control theory and numerical simulation. This study provides a new theoretical framework for the dual strain competition model with different outbreak times. The final theoretical results and numerical simulation showed that although the emergence time of the mutant did not affect the final trend of the epidemic, it would affect the cost of prevention and control during the control period.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant Nos. 12171065, 11671001 and 72171031).

Conflict of interest

The authors declare there are no conflicts of interest.

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