BackgroundThe immunotherapy using dendritic cells (DCs) against different varieties of cancer is an approach that has been previously explored which induces a specific immune response. This work presents a mathematical model of DCs immunotherapy for melanoma in mice based on work by Experimental Immunotherapy Laboratory of the Medicine Faculty in the Universidad Autonoma de Mexico (UNAM).MethodThe model is a five delay differential equation (DDEs) which represents a simplified view of the immunotherapy mechanisms. The mathematical model takes into account the interactions between tumor cells, dendritic cells, naive cytotoxic T lymphocytes cells (inactivated cytotoxic cells), effector cells (cytotoxic T activated cytotoxic cells) and transforming growth factor β cytokine (TGF−β). The model is validated comparing the computer simulation results with biological trial results of the immunotherapy developed by the research group of UNAM.ResultsThe results of the growth of tumor cells obtained by the control immunotherapy simulation show a similar amount of tumor cell population than the biological data of the control immunotherapy. Moreover, comparing the increase of tumor cells obtained from the immunotherapy simulation and the biological data of the immunotherapy applied by the UNAM researchers obtained errors of approximately 10 %. This allowed us to use the model as a framework to test hypothetical treatments. The numerical simulations suggest that by using more doses of DCs and changing the infusion time, the tumor growth decays compared with the current immunotherapy. In addition, a local sensitivity analysis is performed; the results show that the delay in time “ τ”, the maximal growth rate of tumor “r” and the maximal efficiency of tumor cytotoxic cells rate “aT” are the most sensitive model parameters.ConclusionBy using this mathematical model it is possible to simulate the growth of the tumor cells with or without immunotherapy using the infusion protocol of the UNAM researchers, to obtain a good approximation of the biological trials data.It is worth mentioning that by manipulating the different parameters of the model the effectiveness of the immunotherapy may increase. This last suggests that different protocols could be implemented by the Immunotherapy Laboratory of UNAM in order to improve their results.Electronic supplementary materialThe online version of this article (doi:10.1186/s12976-015-0007-0) contains supplementary material, which is available to authorized users.

This paper presents a general property of endoreversible thermal engines known as the Semisum property previously studied in a finite-time thermodynamics context for a Curzon–Ahlborn (CA) engine but now extended to a simplified version of the CA engine studied by Agrawal in 2009 (A simplified version of the Curzon–Ahlborn engine, European Journal of Physics30 (2009), 1173). By building the Ecological function, proposed by Angulo-Brown (An ecological optimization criterion for finite-time heat engines, Journal of Applied Physics69 (1991), 7465–7469) in 1991, and considering two heat transfer laws an analytical expression is obtained for efficiency and power output which depends only on the heat reservoirs’ temperature. When comparing the existing efficiency values of real power plants and the theoretical efficiencies obtained in this work, it is observed that the Semisum property is satisfied. Moreover, for the Newton and the Dulong–Petit heat transfer laws the existence of the g function is demonstrated and we confirm that in a Carnot-type thermal engine there is a general property independent of the heat transfer law used between the thermal reservoirs and the working substance.

Vehicular networks is a key technology for efficiently communicating both user’s devices and cars for timely information regarding safe driving conditions and entertaining applications like social media, video streaming, and gaming services, among others. In view of this, mobile communications making use of cellular resources may not be an efficient and cost-effective alternative. In this context, the implementation of light-fidelity (LiFi) in vehicular communications could be a low-cost, high-data-rate, and efficient-bandwidth usage solution. In this work, we propose a mathematical analysis to study the average throughput in a road intersection equipped with a traffic light that operates as a server, which is assumed to have LiFi communication links with the front lights of the vehicles waiting for the green light. We further assume that the front vehicle (the car next to the traffic light) is able to communicate to the car immediately behind it by using its own tail lights and the front lights of such vehicle, and so on and so forth. The behavior of the road junction is modeled by a Markov chain, applying the Queueing theory with an M/M/1 system in order to obtain the average queue length. Then, Little’s theorem is applied to calculate the average waiting delay when the red light is present in the traffic light. Finally, the mathematical expression of the data throughput is derived.

This work presents a mathematical model to investigate the current outbreak of the coronavirus disease 2019 (COVID-19) worldwide. The model presents the infection dynamics and emphasizes the role of the immune system: both the humoral response as well as the adaptive immune response. We built a mathematical model of delay differential equations describing a simplified view of the mechanism between the COVID-19 virus infection and the immune system. We conduct an analysis of the model exploring different scenarios, and our numerical results indicate that some theoretical immunotherapies are successful in eradicating the COVID-19 virus.

A local stability study of an endoreversible Stefan-Boltzmann (SB) engine, working in a maximum-power-like regime, is presented. This engine consists of a Carnot engine that exchanges heat with heat reservoirs T1 and T2, (T1 > T2) through a couple of thermal links, both having the same conductance g. In addition, the working fluid has the same heat capacity C in the two isothermal branches of the cycle. From the local stability analysis we conclude that the SB engine is stable for every value of g, C and τ = T2/T1. After a small perturbation, the system decays to the steady state with either of two different relaxation times; both being proportional to C/g, and τ . Finally, when we plot some of the thermodynamic properties in the steady state versus τ , we find how an increment of τ can improve the stability of the system, at the same decreasing the efficiency and the power of the system. This suggests a compromise between the stability and the energetic properties of the engine driven by τ .