Class Of Biological Models Research Articles

Traveling waves for reaction-diffusion PDE coupled to difference equation with nonlocal dispersal term and time delay

We consider a class of biological models represented by a system composed of reactiondiffusion PDE coupled with difference equations (renewal equations) in n-dimensional space, with nonlocal dispersal terms and implicit time delays. The difference equation generally arises, by means of the method of characteristics, from an age-structured partial differential system. Using upper and lower solutions, we study the existence of monotonic planar traveling wave fronts connecting the extinction state to the uniform positive state. The corresponding minimum wave speed is also obtained. In addition, we investigate the effect of the parameters on this minimum wave speed and we give a detailed analysis of its asymptotic behavior.

Scaffold-Based and Scaffold-Free Testicular Organoids from Primary Human Testicular Cells.

Organoid systems take advantage of the self-organizing capabilities of cells to create diverse multi-cellular tissue surrogates that constitute a powerful novel class of biological models. Clearly, the formation of a testicular organoid (TO) in which human spermatogenesis can proceed from a single-cell suspension would exert a tremendous impact on research and development, clinical treatment of infertility, and screening of potential drugs and toxic agents. Recently, we showed that primary adult and pubertal human testicular cells auto-assembled in TOs either with or without the support of a natural testis scaffold. These mini-tissues harboured both the spermatogonial stem cells and their important niche cells, which retained certain specific functions during long-term culture. As such, human TOs might advance the development of a system allowing human in vitro spermatogenesis. Here we describe the methodology to make scaffold-based and scaffold-free TOs.

Periodic solutions to a class of biological diffusion models with hysteresis effect

This paper is concerned with a class of biological models which consists of a nonlinear diffusion equation and a hysteresis operator describing the relationship between some variables of the equations. By the viscosity approach, we show the existence of periodic solutions of the problem under consideration. More precisely, with the help of the subdifferential operator theory and Leray–Schauder theorem, we show the existence of periodic solutions to the approximation problem and then obtain the solution of the original problem by using a passage-to-limit procedure.

Well-posedness for a class of biological diffusion models with hysteresis effect

This paper is concerned with a class of biological models which consist of nonlinear diffusion equations and a hysteresis operator describing the relationship between some variables of the equations. The existence of solutions to the analogous problem was ever considered by Aiki and Minchev (SIAM J Math Anal 36:2020–2032, 2005) under some assumptions including the global Lipschitz continuity of reaction terms. We show the existence of nonnegative solutions to the problem under consideration using the approximation method when the reaction terms are locally Lipschitz continuous. Moreover, we discuss the continuous dependence of solutions on initial data.