Dynamical behavior and density function of a stochastic model of HPV infection and cervical cancer with a case study for Xinjiang,China |
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| Institution: | 1. Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology, Nanjing University of Information Science and Technology, Nanjing 210044, China;2. Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin 150001, China;1. Department of Automation, Xiamen University, Xiamen, Fujian 361005, China;2. School of Systems Design and Intelligent Manufacturing, South University of Science and Technology, Shenzhen Guangdong 518000, China;1. Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai 600005, Tamil Nadu, India;2. Indian Institute of Technology - Kanpur, Uttar Pradesh 208016, India;3. CHP-LCOCS, School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China |
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| Abstract: | In this article, combining the transmission features of HPV infection and secondary cervical cancer in Xinjiang, China, a stochastic dynamical model for the HPV infection and secondary cervical cancer with environmental white noise is proposed. Firstly, the stochastic extinction of disease is investigated. A sufficient criterion for the asymptotic behavior of any positive solution of stochastic model revolving around the disease-free equilibrium of corresponding deterministic model is established. Secondly, a threshold criterion for the existence of unique ergodic stationary distribution is obtained by means of the auxiliary function. Furthermore, a new technique of partitioned matrix for the calculation of probability density function is proposed, the expression of a log-normal density function around the quasi-endemic equilibrium of stochastic model is calculated. Lastly, the best-fit parameter values in our model are identified by the MCMC algorithm on the basis of the cervical cancer data in Xinjiang province, China. The basic reproduction number is estimated as 1.3496 (95% CnI: (1.3458, 1.3716)). Then, to determine the key parameters of the model, the sensitivity analysis is explored. Some possible interventions and control measures are provided to reduce the HPV infection spread and cervical cancer in Xinjiang of China. |
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