https://doi.org/10.1140/epjs/s11734-023-00910-9
Regular Article
The impact of media awareness on a fractional-order SEIR epidemic model with optimal treatment and vaccination
1
Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, 711103, Howrah, West Bengal, India
2
Department of Applied Sciences and Humanities, National Institute of Advanced Manufacturing Technology, 834003, Ranchi, Jharkhand, India
3
Department of Mathematics, Ramsaday College, Amta, 711401, Howrah, West Bengal, India
Received:
11
January
2023
Accepted:
2
July
2023
Published online:
26
July
2023
During any pandemic, to decrease the spreading possibility of infectious diseases to people, boosting public awareness is crucial. Media helps to boost this awareness. This paper aims to check the impact of awareness of media regarding infectious diseases. For this reason, an SEIR-type epidemic model is proposed and examined in this research, along with the memory effect. Here, stability analysis and the existence and uniqueness of the non-negative and bounded solution of our model are explored. The basic reproduction number 
is calculated using the next-generation matrix method. Depending on the value of , only one endemic equilibrium occurs and is stable for 
. In addition, it is found that the system encounters a transcritical bifurcation at 
. Here, the optimal treatment and vaccination are determined using the fractional-order optimal control. The findings are also displayed and corroborated by replicating the model with certain hypothetical parameter values, and it can be concluded that fractional order produces better outcomes when the sickness persists in the population. To determine how sensitive the parameters are to and the state variables, we do local and global sensitivity analysis. Sensitivity analysis reveals that by reducing the rates of new recruitment and disease transmission, we might be able to lower the value of . We might be able to retain more susceptibles in the susceptible class by increasing media literacy as well.
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