Stochastic responses of tumor-immune system with periodic treatment

We investigate the stochastic responses of a tumor–immune system competition model with environmental noise and periodic treatment. Firstly, a mathematical model describing the interaction between tumor cells and immune system under external fluctuations and periodic treatment is established based on the stochastic differential equation. Then, sufficient conditions for extinction and persistence of the tumor cells are derived by constructing Lyapunov functions and Ito＇s formula. Finally, numerical simulations are introduced to illustrate and verify the results. The results of this work provide the theoretical basis for designing more effective and precise therapeutic strategies to eliminate cancer cells, especially for combining the immunotherapy and the traditional tools.

Performance Analysis of Intelligent Robust Facility Layout Design

Design of a robust production facility layout with minimum handling cost （MHC） presents an appropriate approach to tackle facility layout problems in a dynamic volatile environment, in which product demands randomly change in each planning period. The objective of the design is to find the robust facility layout with minimum total material handling cost over the entire multiperiod planning horizon. This paper proposes a new mathematical model for designing robust machine layout in the stochastic dynamic environment of manufacturing systems using quadratic assignment problem （QAP） formulation. In this investigation, product demands are assumed to be normally distributed random variables with known expected value, variance, and covariance that randomly change from period to period. The proposed model was verified and validated using randomly generated numerical data and benchmark examples. The effect of dependent product demands and varying interest rate on the total cost function of the proposed model has also been investigated. Sensitivity analysis on the proposed model has been performed. Dynamic programming and simulated annealing optimization algorithms were used in solving the modeled example problems.

The role of weather and density dependence on population dynamics of Alpine-dwelling red deer

The dynamics of red deer Cervus elaphus populations has been investigated across different environmental conditions,with the notable exception of the European Alps.Although the population dynamics of mountain-dwelling ungulates is typically influenced by the interaction between winter severity and density,the increase of temperatures and the reduction of snowpack occurring on the Alps since the 1980s may be expected to alter this pattern,especially in populations dwelling at medium-low elevations.Taking advantage of a 29-year time series of spring count data,we explored the role of weather stochasticity and density dependence on growth rate and vital rates(mortality and weaning success),and the density-dependent variation in body mass in a red deer population of the Italian Alps.The interaction between increasing values of density and snow depth exerted negative and positive effects on growth and mortality rates,respectively,while weaning success was negatively affected by increasing values of density,female-biased sex ratio and snow depth.Body mass of males and females of different age classes declined as population size increased.Our data support the role of winter severity and density dependence as key components of red deer population dynamics,and provide insight into the species’ecology on the European Alps.Despite the recent decline of snowpack on the Alpine Region,the negative impacts of winter severity and population abundance on growth rrate(possibly mediated by the density-dependent decline in body mass)confirms the importance of overwinter mortality in affecting the population dynamics of Alpine-dwelling red deer.