Dynamical Analysis of a Stochastic Cholera Epidemic Model

Xueyong Zhou ()
Additional contact information
Xueyong Zhou: School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China

Mathematics, 2022, vol. 10, issue 16, 1-19

Abstract: Environmental disturbances have a strong impact on cholera transmission. Stochastic differential equations are an effective tool for characterizing environmental perturbations. In this paper, a stochastic infectious disease model for cholera is established and investigated. The dynamics of the stochastic cholera model are discussed. Firstly, the existence and uniqueness of the positive solution are proven. Then, the asymptotical stability of the disease-free equilibrium of the system is investigated. Furthermore, the asymptotical stability of the endemic equilibrium of the deterministic system corresponding to the stochastic system is obtained. Then, the theoretical results are verified by some numerical simulations. Finally, the optimal problem is considered as the theoretical basis for the control of cholera. Both theoretical and numerical results indicate that the random perturbations may make the model more realistic, which provides theoretical assessment for the control of cholera transmission.

Keywords: stochastic epidemic model; cholera; asymptotic stability; optimal control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/16/2830/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/16/2830/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:16:p:2830-:d:883924

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().