In this paper, we develop a non-local mathematical model describing cancer cell invasion and movement as a result of integrin-controlled cell-cell adhesion and cell-matrix adhesion, and transforming growth factor-beta (TGF-β) effect on cell proliferation and adhesion, for two cancer cell populations with different levels of mutation. The model consists of partial integro-differential equations describing the dynamics of two cancer cell populations, coupled with ordinary differential equations describing the extracellular matrix (ECM) degradation and the production and decay of integrins, and with a parabolic PDE governing the evolution of TGF-β concentration. We prove the global This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC-BY) License. Further distribution of this work is permitted, provided the original work is properly cited.

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.

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.

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.