The measles epidemic model assessment under real statistics: an application of stochastic optimal control theory

Abstract

A stochastic epidemic model with random noise transmission is taken into account, describing the dynamics of the measles viral infection. The basic reproductive number is calculated corresponding to the stochastic model. It is determined that, given initial positive data, the model has bounded, unique, and positive solution. Additionally, utilizing stochastic Lyapunov functional theory, we study the extinction of the disease. Stationary distribution and extinction of the infection are examined by providing sufficient conditions. We employed optimal control principles and examined stochastic control systems to regulate the transmission of the virus using environmental factors. Graphical representations have been offered for simplicity of comprehending in order to further verify the acquired analytical findings.

Keywords:

• Stochastic epidemic model
• threshold value
• real data
• stationary distribution
• extinction
• stochastic optimal control

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was funded by the National Natural Science Foundation for the People’s Republic of China (Nos. 11901114 and 11801073), the Guangzhou Science and Technology Innovation General Project (No. 201904010010), the Guangdong Provincial Department of Education’s Young Innovative Talents Project (No. 2017KQNCX081), and the Natural Science Foundation of Guangdong Province (Grant No. 2017A030310598).