A Mathematical Study of the Role of tBregs in Breast Cancer.

A model for the mathematical study of immune response to breast cancer is proposed and studied, both analytically and numerically. It is a simplification of a complex one, recently introduced by two of the present authors. It serves for a compact study of the dynamical role in cancer promotion of a relatively recently described subgroup of regulatory B cells, which are evoked by the tumour.

Mathematical modeling of tumor-immune system interactions: the effect of rituximab on breast cancer immune response.

tBregs are a newly discovered subcategory of B regulatory cells, which are generated by breast cancer, resulting in the increase of Tregs and therefore in the death of NK cells. In this study, we use a mathematical and computational approach to investigate the complex interactions between the aforementioned cells as well as CD8+ T cells, CD4+ T cells and B cells. Furthermore, we use data fitting to prove that the functional response regarding the lysis of breast cancer cells by NK cells has a ratio-dependent form. Additionally, we include in our model the concentration of rituximab - a monoclonal antibody that has been suggested as a potential breast cancer therapy - and test its effect, when the standard, as well as experimental dosages, are administered.

New insights about vaccine effectiveness: Impact of attenuated PRRS-strain vaccination on heterologous strain transmission.

Vaccination is the main tool for controlling infectious diseases in livestock. Yet current vaccines only provide partial protection raising concerns about vaccine effectiveness in the field. Two successive transmission trials were performed involving 52 pigs to evaluate the effectiveness of a Porcine Reproductive and Respiratory Syndrome (PRRS) vaccinal strain candidate against horizontal transmission of a virulent heterologous strain. PRRS virus, above the specified limit of detection, was observed in serum and nasal secretions for all but one pig (the exception only tested positive for serum), indicating that vaccination did not protect pigs from becoming infected and shedding the heterologous strain. However, vaccination delayed the onset of viraemia, reduced the duration of shedding and significantly decreased viral load throughout infection. Serum antibody profiles indicated that 4 out of 13 (31%) vaccinates in one trial had no serological response (NSR). A Bayesian epidemiological model was fitted to the data to assess the impact of vaccination and presence of NSRs on PRRS virus transmission dynamics. Despite little evidence for reduction in the transmission rate, vaccinated animals were on average slower to become infectious, experienced a shorter infectious period and recovered faster. The overall PRRSV transmission potential, represented by the reproductive ratio R0 was lower for the vaccinated animals, although there was substantial overlap in the credibility intervals for both groups. Model selection suggests that transmission parameters of vaccinated pigs with NSR were more similar to those of unvaccinated animals. The presence of NSRs in a population, however, seemed to only marginally affect the transmission dynamics. The results suggest that even when vaccination can't prevent infection, it can still have beneficial impacts on the transmission dynamics and contribute to reducing a herd's R0. However, biosecurity and other measures need to be considered to decrease contact rates and lower R0 below 1.

Predicting vaccine effectiveness in livestock populations: A theoretical framework applied to PRRS virus infections in pigs.

Vaccines remain one of the main tools to control infectious diseases in domestic livestock. Although a plethora of veterinary vaccines are on the market and routinely applied to protect animals against infection with particular pathogens, the disease in question often continues to persist, sometimes at high prevalence. The limited effectiveness of certain vaccines in the field leaves open questions regarding the required properties that an effective vaccine should have, as well as the most efficient vaccination strategy for achieving the intended goal of vaccination programmes. To date a systematic approach for studying the combined effects of different types of vaccines and vaccination strategies is lacking. In this paper, we develop a theoretical framework for modelling the epidemiological consequences of vaccination with imperfect vaccines of various types, administered using different strategies to herds with different replacement rates and heterogeneity in vaccine responsiveness. Applying the model to the Porcine Reproductive and Respiratory Syndrome (PRRS), which despite routine vaccination remains one of the most significant endemic swine diseases worldwide, we then examine the influence of these diverse factors alone and in combination, on within-herd virus transmission. We derive threshold conditions for preventing infection invasion in the case of imperfect vaccines inducing limited sterilizing immunity. The model developed in this study has practical implications for the development of vaccines and vaccination programmes in livestock populations not only for PRRS, but also for other viral infections primarily transmitted by direct contact.

Non-local Parabolic and Hyperbolic Models for Cell Polarisation in Heterogeneous Cancer Cell Populations.

Tumours consist of heterogeneous populations of cells. The sub-populations can have different features, including cell motility, proliferation and metastatic potential. The interactions between clonal sub-populations are complex, from stable coexistence to dominant behaviours. The cell-cell interactions, i.e. attraction, repulsion and alignment, processes critical in cancer invasion and metastasis, can be influenced by the mutation of cancer cells. In this study, we develop a mathematical model describing cancer cell invasion and movement for two polarised cancer cell populations with different levels of mutation. We consider a system of non-local hyperbolic equations that incorporate cell-cell interactions in the speed and the turning behaviour of cancer cells, and take a formal parabolic limit to transform this model into a non-local parabolic model. We then investigate the possibility of aggregations to form, and perform numerical simulations for both hyperbolic and parabolic models, comparing the patterns obtained for these models.

Aggregation and travelling wave dynamics in a two-population model of cancer cell growth and invasion.

Cells adhere to each other and to the extracellular matrix (ECM) through protein molecules on the surface of the cells. The breaking and forming of adhesive bonds, a process critical in cancer invasion and metastasis, can be influenced by the mutation of cancer cells. In this paper, we develop a nonlocal mathematical model describing cancer cell invasion and movement as a result of integrin-controlled cell-cell adhesion and cell-matrix adhesion, for two cancer cell populations with different levels of mutation. The partial differential equations for cell dynamics are coupled with ordinary differential equations describing the ECM degradation and the production and decay of integrins. We use this model to investigate the role of cancer mutation on the possibility of cancer clonal competition with alternating dominance, or even competitive exclusion (phenomena observed experimentally). We discuss different possible cell aggregation patterns, as well as travelling wave patterns. In regard to the travelling waves, we investigate the effect of cancer mutation rate on the speed of cancer invasion.