Stochastic analysis for measles transmission with Lévy noise: a case study

Asad Khan; Anwarud Din; Asad Khan; Anwarud Din

doi:10.3934/math.2023952

AIMS Mathematics

2023, Volume 8, Issue 8: 18696-18716. doi: 10.3934/math.2023952

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Research article

Stochastic analysis for measles transmission with Lévy noise: a case study

Asad Khan ^{1
,
,},
Anwarud Din ^{2
,
,}

1.
School of Computer Science and Cyber Engineering, Guangzhou University, Guangzhou 510006, China
2.
Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China

Received: 02 April 2023 Revised: 10 May 2023 Accepted: 16 May 2023 Published: 02 June 2023
MSC : 60J65, 60E05, 60K37

In this paper, we deal with a Lévy noise-driven epidemic model reflecting the dynamics of measles infection subject to the effect of vaccination. After model formulation, the feasibility of the system was studied by using the underlying existence and uniqueness theory. Moreover, we discussed the behavior of solution around the infection-free and disease-present steady states. To check the persistence and extinction of the infection, we calculated the threshold parameter $ {\bf R_s} $ and it was determined that the disease vanishes whenever $ {\bf R_s} < 1 $. From January to October 2019, the reported measles cases in Pakistan wear used and the model was fitted against this data by using the well-known fitting techniques. The values of the parameter were estimated and future behavior of the infection was predicted by simulating the model. The model was further simulated and theoretical findings of the study were validated.
- white noise,
- Lévy jump,
- Lyapunov function,
- persistence,
- parameter estimation,
- positive recurrence
Citation: Asad Khan, Anwarud Din. Stochastic analysis for measles transmission with Lévy noise: a case study[J]. AIMS Mathematics, 2023, 8(8): 18696-18716. doi: 10.3934/math.2023952

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Abstract

In this paper, we deal with a Lévy noise-driven epidemic model reflecting the dynamics of measles infection subject to the effect of vaccination. After model formulation, the feasibility of the system was studied by using the underlying existence and uniqueness theory. Moreover, we discussed the behavior of solution around the infection-free and disease-present steady states. To check the persistence and extinction of the infection, we calculated the threshold parameter $ {\bf R_s} $ and it was determined that the disease vanishes whenever $ {\bf R_s} < 1 $. From January to October 2019, the reported measles cases in Pakistan wear used and the model was fitted against this data by using the well-known fitting techniques. The values of the parameter were estimated and future behavior of the infection was predicted by simulating the model. The model was further simulated and theoretical findings of the study were validated.

References

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