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Advances in Continuous and Discrete Models

Theory and Modern Applications

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  3. In this study, we develop a stochastic model that captures the dynamics of HIV infection, encompassing susceptible individuals, asymptomatic HIV-positive individuals, and those exhibiting symptoms. Initially, ...

    Authors: Feng Rao, Yiping Tan and Xinze Lian
    Citation: Advances in Continuous and Discrete Models 2025 2025:38
    Content type: Research Published on:

  4. This paper considers a stochastic model of microorganism flocculation incorporating two complementary nutrients. By introducing nonlinear perturbation, we analyze the influence of flocculations, microorganisms...

    Authors: Donghong Zhao, Jiajia Duan, Rong Liu and Ke Guo
    Citation: Advances in Continuous and Discrete Models 2025 2025:37
    Content type: Research Published on:

  6. This study investigates strategies for accelerating mosquito population replacement through the periodic release of Wolbachia-infected male mosquitoes using a two-dimensional time-switching model. We obtain the e...

    Authors: Hongpeng Guo
    Citation: Advances in Continuous and Discrete Models 2025 2025:35
    Content type: Research Published on:

  7. We investigate the comprehensive impact of dynamic changes in CEA (carcinoembryonic antigen) and E2 (estradiol) values on the survival prognosis of breast cancer patients in Xinjiang, as well as predict their lon...

    Authors: Tao Ma, Chunjie Gao, Yipala Yilihamu, Jing Liu, Ting Zhao and Lei Wang
    Citation: Advances in Continuous and Discrete Models 2025 2025:34
    Content type: Research Published on:

  10. To understand the impact of vaccination, we consider an SIVR (susceptible–infected–vaccinated–recovered) model that combines impulsive vaccination into the classical SIR model. The final size is firstly define...

    Authors: Phyu Phyu Win, Zhigui Lin and Mengyun Zhang
    Citation: Advances in Continuous and Discrete Models 2025 2025:31
    Content type: Research Published on:

  12. In this paper, we investigate the spatiotemporal dynamics of a fractional-order predator-prey reaction-diffusion model (frPDE) with Holling-type III functional response. We prove that this is not the integer-o...

    Authors: Zhaohua Wu, Zhiming Wang, Yongli Cai, Hongwei Yin and Weiming Wang
    Citation: Advances in Continuous and Discrete Models 2025 2025:29
    Content type: Research Published on:

  14. The stability of predator–prey interactions in ecosystems is influenced by both inherent species interactions and external factors. For instance, the presence of additional food, as an external factor, may aff...

    Authors: Huazhou Mo and Yuanfu Shao
    Citation: Advances in Continuous and Discrete Models 2025 2025:27
    Content type: Research Published on:

  15. In this study, a predator–prey model incorporating prey’s fear effect and anti-predation behavior has been developed. The functional response takes the square root of the prey population and adds the predator’...

    Authors: Minghao Yang, Changcheng Xiang and Yi Yang
    Citation: Advances in Continuous and Discrete Models 2025 2025:26
    Content type: Research Published on:

  16. In the present paper we study the existence and stability problems of positive periodic solutions to a Gilpin–Ayala competitive model with periodic coefficients on time scales. Firstly, based on Schauder’s fix...

    Authors: Shihong Zhu, Xiaoliang Li and Bo Du
    Citation: Advances in Continuous and Discrete Models 2025 2025:25
    Content type: Research Published on:

  17. Exploring the dynamics of the CD4+ T regulatory network holds paramount significance in scientific research, as it deepens our understanding of the immune system’s intricacies and drives the development of inn...

    Authors: Xiaoqi Lu, Qing Hu, Zhuozhen Xue and Ruiqi Wang
    Citation: Advances in Continuous and Discrete Models 2025 2025:24
    Content type: Research Published on:

  21. In this paper, a delayed double-strain influenza model with vaccination and cross-immunity is proposed to explore the effect of coinfection of double-strain on disease spread. First, the nonnegativity and ulti...

    Authors: Shukun Gao, Long Zhang, Hongli Li and Zhidong Teng
    Citation: Advances in Continuous and Discrete Models 2025 2025:20
    Content type: Research Published on:

  22. In this paper, we investigate a delayed diffusive predator–prey model with weak Allee effect for predator. First, we discuss the existence and uniqueness of positive steady state and the local Hopf bifurcation...

    Authors: Xiaohui Zhang, Xiaofeng Xu and Ming Liu
    Citation: Advances in Continuous and Discrete Models 2025 2025:19
    Content type: Research Published on:

  24. The burden of influenza virus infection poses a challenge due to its significant negative impact on public health. The implementation of intervention measures including vaccination, treatment, and isolation ca...

    Authors: Xiaomeng Wang and Yongli Cai
    Citation: Advances in Continuous and Discrete Models 2025 2025:17
    Content type: Research Published on:

  25. In this paper, in order to study comprehensive effect of stage-structure, incomplete immunity and spatial diffusion on the transmission dynamics of sheep brucellosis, we formulate a reaction-diffusion brucello...

    Authors: Tingting Zheng, Yicheng Hao, Yantao Luo and Zhidong Teng
    Citation: Advances in Continuous and Discrete Models 2025 2025:16
    Content type: Research Published on:

  26. A nonautonomous periodic discrete model is proposed to characterize the dynamics of Wolbachia spread in mosquito populations under period-2 environments, where the Wolbachia strain in the first environment is les...

    Authors: Huifen Luo, Huichao Yang, Jianshe Yu and Bo Zheng
    Citation: Advances in Continuous and Discrete Models 2025 2025:15
    Content type: Research Published on:

  28. In view of the importance of predator-dependent functional response and fear of prey induced by powerful predators, we construct a delayed prey–predator model with fear and Beddington–DeAngelis functional resp...

    Authors: Jinxing Zhao and Yuanfu Shao
    Citation: Advances in Continuous and Discrete Models 2025 2025:13
    Content type: Research Published on:

  30. Incorporating stochastic processes into biological models is crucial for capturing the inherent variability and uncertainties within biological systems. This paper explores the benefits of introducing Black–Ka...

    Authors: Zhongwei Cao, Zhenfeng Shi, Zhifei Song, Li Zu and Hewei Xu
    Citation: Advances in Continuous and Discrete Models 2025 2025:11
    Content type: Research Published on:

  33. Gestation is a very significant phenomenon in predator-prey dynamics. It influences the future predation rates and the growth of species. Gestation is the period of development of an embryo or fetus in a femal...

    Authors: Bipin Kumar, Rajesh Kumar Sinha and Saddam Hussain
    Citation: Advances in Continuous and Discrete Models 2025 2025:8
    Content type: Research Published on:

  34. Actual cancer treatment is typically a dynamic process with stochastic disturbances. Uncertain constraints (UCs) are suitable for modeling of dynamic processes under stochastic disturbance conditions, in which...

    Authors: Xiang Wu, Xiaolan Yuan and Kanjian Zhang
    Citation: Advances in Continuous and Discrete Models 2025 2025:7
    Content type: Research Published on:

  35. This article investigates the role of problem representation in complex problem-solving based on quasi-experimental data analysis, specifically within the context of computational thinking. Using the Tower of ...

    Authors: Jinlong Fei, Shuyuan Dong and Dingzhou Fei
    Citation: Advances in Continuous and Discrete Models 2025 2025:6
    Content type: Research Published on:

  36. Unlike many countries that have experienced multiple COVID-19 waves since January 2020, China’s stringent measures left most of the population without natural immunity to SARS-CoV-2. After lifting controls, Ch...

    Authors: Yepeng Shi, Qiuying Lv, Kemin Zhu, Jun Cai, Dongfeng Kong, Kang Liu, Zhigao Chen, Zhen Zhang and Ling Yin
    Citation: Advances in Continuous and Discrete Models 2025 2025:5
    Content type: Research Published on:

  37. The existence-uniqueness theory for solutions to stochastic dynamic systems is always a significant theme and has received tremendous attention. This article aims to study the theory for stochastic functional ...

    Authors: Rahman Ullah, Faiz Faizullah, Ihteram Ali, Muhammad Farooq, M. A. Rana and Fuad A. Awwad
    Citation: Advances in Continuous and Discrete Models 2025 2025:4
    Content type: Research Published on:

  39. The goal of this paper is to present a second-order finite difference scheme for Allen–Cahn equations with Riesz fractional derivative. The discrete maximum bound principle, the maximum-norm error estimates, a...

    Authors: Changling Xu, Yang Cao and Tianliang Hou
    Citation: Advances in Continuous and Discrete Models 2025 2025:2
    Content type: Research Published on:

  41. Cell-to-cell infection cannot be ignored in the development of HIV in the host. The mathematical difficulty in (Wang et al. in J. Biol. Dyn. 11:455–483, 2016) is mainly due to the assumption of the equality of tw...

    Authors: Zhigang Liu and Tiejun Zhou
    Citation: Advances in Continuous and Discrete Models 2024 2024:60
    Content type: Research Published on:

  43. The frequent emergence of new infectious diseases poses a serious threat to human health and social development. In the current digital age, the widespread application of online social networks has accelerated...

    Authors: Li Yan and Zhen Han
    Citation: Advances in Continuous and Discrete Models 2024 2024:61
    Content type: Research Published on:

  45. A general stochastic compartment model for cholera with higher-order perturbation is proposed, which incorporates direct and indirect transmission by contaminated water. Nonlinear incidence, multiple stages of...

    Authors: Wenjie Zuo, Beibei Liao, Junyan Ge, Na Zhao and Daqing Jiang
    Citation: Advances in Continuous and Discrete Models 2024 2024:57
    Content type: Research Published on:

  46. The world citrus industry is confronting an unprecedented challenge from citrus Huanglongbing (HLB). With no resistant commercial citrus varieties or curable chemicals currently available, HLB remains the top ...

    Authors: Youquan Luo, Shuimei Tang, Fumin Zhang, Yujiang Liu and Shujing Gao
    Citation: Advances in Continuous and Discrete Models 2024 2024:56
    Content type: Research Published on:

  48. This study establishes a novel three-species host–parasitoid–hyperparasitoid system with mutual interference effects on parasitoids and hyperparasitoids. We derive the asymptotic stability conditions for the e...

    Authors: Lijiao Jia and Il Hyo Jung
    Citation: Advances in Continuous and Discrete Models 2024 2024:54
    Content type: Research Published on:

  49. In this paper, we propose a reaction-diffusion SIRC model with cross-immunization. The model includes the implementation of vaccination measures for susceptible, and treatment and quarantine measures for infec...

    Authors: Pan Zhou, Jianpeng Wang, Zhidong Teng, Yanling Zheng and Kai Wang
    Citation: Advances in Continuous and Discrete Models 2024 2024:53
    Content type: Research Published on:

  50. In this paper, we investigate an approximative maximum likelihood estimator (MLE) for the drift coefficient of a stochastic partial differential equation in the case where the corresponding Fourier coefficients

    Authors: Abdulaziz Alsenafi, Fares Alazemi and Khalifa Es-Sebaiy
    Citation: Advances in Continuous and Discrete Models 2024 2024:52
    Content type: Research Published on:
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Annual Journal Metrics

  • Citation Impact 2023
    Journal Impact Factor: 3.1
    5-year Journal Impact Factor: 2.3
    Source Normalized Impact per Paper (SNIP): 1.007
    SCImago Journal Rank (SJR): 0.504

    Speed 2024
    Submission to first editorial decision (median days): 13
    Submission to acceptance (median days): 91

    Usage 2024
    Downloads: 1,478,630
    Altmetric mentions: 13

  • ISSN: 2731-4235 (electronic)