我们从确定性模型开始，提出并研究了人乳头瘤病毒感染和宫颈癌进展的随机模型。我们的分析表明，慢性感染状态作为具有遍历不变概率测度的随机变量对于从受感染细胞群进展到宫颈癌细胞是必要的。研究表明，从感染细胞到癌前细胞的进展速度较小，以及与进展速度和病毒感染相关的微环境噪音较小，有助于建立这种慢性感染状态。这意味着与病毒感染和体内进展速度相关的大环境噪音可以减少慢性感染。我们进一步表明，如果与癌前细胞生长相关的噪音足够大，就会出现宫颈癌。此外，确定性模型和随机模型的可比数值研究，以及确定性和随机系统中的 Hopf 分岔，突出了我们的分析结果。© 2023。作者获得 Springer-Verlag GmbH 德国的独家许可，部分施普林格自然。

Starting from a deterministic model, we propose and study a stochastic model for human papillomavirus infection and cervical cancer progression. Our analysis shows that the chronic infection state as random variables which have the ergodic invariant probability measure is necessary for progression from infected cell population to cervical cancer cells. It is shown that small progression rate from infected cells to precancerous cells and small microenvironmental noises associated with the progression rate and viral infection help to establish such chronic infection states. It implicates that large environmental noises associated with viral infection and the progression rate in vivo can reduce chronic infection. We further show that there will be a cervical cancer if the noise associated with precancerous cell growth is large enough. In addition, comparable numerical studies for the deterministic model and stochastic model, together with Hopf bifurcations in both deterministic and stochastic systems, highlight our analytical results.© 2023. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.