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<abstract><p>Cancer is recognized as one of the serious diseases threatening human health. Oncolytic therapy is a safe and effective new cancer treatment method. Considering the limited ability of uninfected tumor cells to infect and the age of infected tumor cells have a significant effect on oncolytic therapy, an age-structured model of oncolytic therapy involving Holling-Ⅱ functional response is proposed to investigate the theoretical significance of oncolytic therapy. First, the existence and uniqueness of the solution is obtained. Furthermore, the stability of the system is confirmed. Then, the local stability and global stability of infection-free homeostasis are studied. The uniform persistence and local stability of the infected state are studied. The global stability of the infected state is proved by constructing the Lyapunov function. Finally, the theoretical results are verified by numerical simulation. The results show that when the tumor cells are at the appropriate age, injection of the right amount of oncolytic virus can achieve the purpose of tumor treatment.</p></abstract>

In this paper, we present and analyze an age-structured tumor immune model. Based on the fact that tumor cells of different ages tend to exhibit different physiological behaviors, we consider the age structure of tumor cells, age-based proliferation function and age-dependent death function in the model. The threshold $\mathfrak{R}_{0}$ for the existence of tumor-free steady state is derived. It is found that if $\mathfrak{R}_{0}<1$, the tumor-free steady state is not only locally stable but also globally stable. Moreover, numerical simulation shows that the threshold $\mathfrak{R}_{0}$ may be regarded as an index to reflect the ability of ``tumor immune surveillance", \ie, the smaller the $\mathfrak{R}_{0}$, the better the ability of tumor immune surveillance. If $\mathfrak{R}_{0}>1$, it is proved that the tumor steady state is existent  and uniformly persistent. The local stability of the tumor steady state is investigated under some further conditions besides $\mathfrak{R}_{0}>1$. In the end, we estimate the system parameters, verify the theoretical results and analyze some system  parameters' sensitivities.

Cobble size distribution (CSD) on the surface of a cobble bed is an important part of the river system, with important implications for river ecology and geomorphology. A digital image edge detection algorithm based on markers and detection lines is proposed to realize automatic statistics gathering of CSD. By making multiple detection lines outward from the markers, the cobble edge detection process of 2D images is transformed into a 1D space for analysis and processing. To correct the error detection points, an edge correction algorithm based on mutation point detection is designed. Simultaneously, a cobble edge reconstruction algorithm is proposed to restore covered cobble edges. The results of a verification experiment and comparative analysis indicate that the relative error of D 50 , which was estimated by the algorithm in our study, is 3% in the laboratory and 8% in the field. The proposed method is reliable for the estimation of CSD with grain size range of 5 to 50 cm. In conclusion, the proposed algorithm is suitable for river geomorphology research and physical habitat studies of cobble floodplains using an unmanned aerial vehicle for remote sensing photography.