Multiple sclerosis (MS) is a neurodegenerative disease in which misdirected, persistent activity of the immune system degrades the protective myelin sheaths of nerve axons. Historically, treatment of MS has relied on disease-modifying therapies that involve immunosuppression, such as targeting of the blood-brain barrier (BBB) to restrict lymphocyte movement. New therapeutic ideas in the development pipeline are instead designed to promote populations of myelin producing cells, oligodendrocytes, by exploiting their innate resilience to the stressors of MS or restoring their numbers. Given the significant advancements made in immunological disease understanding due to mathematical and computational modelling, we sought to develop a platform to (1) interrogate our understanding of the neuroimmunological mechanisms driving MS development and (2) examine the impact of different therapeutic strategies. To this end we propose a novel, open-source, agent-based model of lesion development in the CNS. Our model includes crucial populations of T cells, perivascular macrophages, and oligodendrocytes. We examine the sensitivity of the model to key parameters related to disease targets and conclude that lesion stabilisation can be achieved when targeting the integrated stress response of oligodendrocytes. Most significantly, complete prevention of lesion formation is observed when a combination of approved BBB-permeability targeting therapies and integrated-stress response targeting therapies is administered, suggesting the potential to strike a balance between a patient's immune inflammation and their reparative capacity. Given that there are many open questions surrounding the etiology and treatment of MS, we hope that this malleable platform serves as a tool for experimentalists and modellers to test and generate further hypotheses regarding this disease.

Phenotypic plasticity contributes significantly to treatment failure in many cancers. Despite the increased prevalence of experimental studies that interrogate this phenomenon, there remains a lack of applicable quantitative tools to characterise data, and importantly to distinguish between resistance as a discrete phenotype and a continuous distribution of phenotypes. To address this, we develop a stochastic individual-based model of plastic phenotype adaptation through a continuously-structured phenotype space in low-cell-count proliferation assays. That our model corresponds probabilistically to common partial differential equation models of resistance allows us to formulate a likelihood that captures the intrinsic noise ubiquitous to such experiments. We apply our framework to assess the identifiability of key model parameters in several population-level data collection regimes; in particular, parameters relating to the adaptation velocity and cell-to-cell heterogeneity. Significantly, we find that cell-to-cell heterogeneity is practically non-identifiable from both cell count and proliferation marker data, implying that population-level behaviours may be well characterised by homogeneous ordinary differential equation models. Additionally, we demonstrate that population-level data are insufficient to distinguish resistance as a discrete phenotype from a continuous distribution of phenotypes. Our results inform the design of both future experiments and future quantitative analyses that probe phenotypic plasticity in cancer.

The COVID-19 pandemic caused by the severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) resulted in millions of deaths globally. Adults with immunosuppression (e.g., solid organ transplant recipients) and those undergoing active cancer treatments experience worse infections and more severe COVID-19. It is difficult to conduct clinical studies in these populations, resulting in a restricted amount of data that can be used to relate mechanisms of immune dysfunction to COVID-19 outcomes in these vulnerable groups. To study immune dynamics after infection with SARS-CoV-2 and to investigate drivers of COVID-19 severity in individuals with cancer and immunosuppression, we adapted our mathematical model of the immune response during COVID-19 and generated virtual patient cohorts of cancer and immunosuppressed patients. The cohorts of plausible patients recapitulated available longitudinal clinical data collected from patients in Montréal, Canada area hospitals. Our model predicted that both cancer and immunosuppressed virtual patients with severe COVID-19 had decreased CD8 + T cells, elevated interleukin-6 concentrations, and delayed type I interferon peaks compared to those with mild COVID-19 outcomes. Additionally, our results suggest that cancer patients experience higher viral loads (however, with no direct relation with severity), likely because of decreased initial neutrophil counts (i.e., neutropenia), a frequent toxic side effect of anti-cancer therapy. Furthermore, severe cancer and immunosuppressed virtual patients suffered a high degree of tissue damage associated with elevated neutrophils. Lastly, parameter values associated with monocyte recruitment by infected cells were found to be elevated in severe cancer and immunosuppressed patients with respect to the COVID-19 reference group. Together, our study highlights that dysfunctions in type I interferon and CD8 + T cells are key drivers of immune dysregulation in COVID-19, particularly in cancer patients and immunosuppressed individuals.

The prognosis for pancreatic ductal adenocarcinoma (PDAC) patients has not significantly improved in the past 3 decades, highlighting the need for more effective treatment approaches. Poor patient outcomes and lack of response to therapy can be attributed, in part, to a lack of uptake of perfusion of systemically administered chemotherapeutic drugs into the tumour. Wet-spun alginate fibres loaded with the chemotherapeutic agent gemcitabine have been developed as a potential tool for overcoming the barriers in delivery of systemically administrated drugs to the PDAC tumour microenvironment by delivering high concentrations of drug to the tumour directly over an extended period. While exciting, the practicality, safety, and effectiveness of these devices in a clinical setting requires further investigation. Furthermore, an in-depth assessment of the drug-release rate from these devices needs to be undertaken to determine whether an optimal release profile exists. Using a hybrid computational model (agent-based model and partial differential equation system), we developed a simulation of pancreatic tumour growth and response to treatment with gemcitabine loaded alginate fibres. The model was calibrated using in vitro and in vivo data and simulated using a finite volume method discretisation. We then used the model to compare different intratumoural implantation protocols and gemcitabine-release rates. In our model, the primary driver of pancreatic tumour growth was the rate of tumour cell division. We were able to demonstrate that intratumoural placement of gemcitabine loaded fibres was more effective than peritumoural placement. Additionally, we quantified the efficacy of different release profiles from the implanted fibres that have not yet been tested experimentally. Altogether, the model developed here is a tool that can be used to investigate other drug delivery devices to improve the arsenal of treatments available for PDAC and other difficult-to-treat cancers in the future.

Heterogeneity is a dominant factor in the behaviour of many biological processes. Despite this, it is common for mathematical and statistical analyses to ignore biological heterogeneity as a source of variability in experimental data. Therefore, methods for exploring the identifiability of models that explicitly incorporate heterogeneity through variability in model parameters are relatively underdeveloped. We develop a new likelihood-based framework, based on moment matching, for inference and identifiability analysis of differential equation models that capture biological heterogeneity through parameters that vary according to probability distributions. As our novel method is based on an approximate likelihood function, it is highly flexible; we demonstrate identifiability analysis using both a frequentist approach based on profile likelihood, and a Bayesian approach based on Markov-chain Monte Carlo. Through three case studies, we demonstrate our method by providing a didactic guide to inference and identifiability analysis of hyperparameters that relate to the statistical moments of model parameters from independent observed data. Our approach has a computational cost comparable to analysis of models that neglect heterogeneity, a significant improvement over many existing alternatives. We demonstrate how analysis of random parameter models can aid better understanding of the sources of heterogeneity from biological data.