ICTS

Francisella tularensis is a highly infectious bacterium capable of causing a debilitating disease with as few as 10 organisms, and is currently classified as a category A biothreat agent. To study disease progression, we begin with a stochastic model of a population of infectious agents inside a single host cell. Different approaches are considered to determine the time until rupture of an infected macrophage and the number of bacteria released when the cell bursts. From a single-cell model we are able to approximate well the dynamics within the lung of an infected mice, comparing our results with those of agent-based computation. Further comparisons with experimental measurements, carried out after murine aerosol infection with the virulent SCHU S4 strain, enable us to infer model parameters using Approximate Bayesian Computation (ABC), obtaining a bacterial growth rate that is consistent previous beliefs that the time between rounds of infection is less than 6 hours in vivo

The ability of bacteria to become resistant to previously successful antibiotic treatments is an urgent and increasing worldwide problem. Solutions can be sought via a number of methods including, for example, identifying novel antibiotics, re-engineering existing antibiotics or developing alternative treatment methods. The nonlinear interactions involved in infection and treatment render it difficult to predict the success of any of these methods without the use of computational tools in addition to more traditional experimental work. We use mathematical modelling to aid in the development of anti-virulence treatments which, unlike conventional antibiotics that directly target a bacterium’s survival, may instead attenuate bacteria and prevent them from being able to cause infection. Many of these approaches, however, are only partially successful when tested in infection models. We present two such potential treatments in relation to the multi-drug resistant bacterium Pseudomonas aeruginosa: targeting host-cell adhesion and cell-morphology transitions that facilitate persister-like behaviour. Using mathematical modelling we consider ways to optimise the efficacy of such treatments.

Measles was eliminated, meaning an end to continuous transmission, from the US in 2000. However, outbreaks continue to occur due to introductions from international travel. Measles immunization is mandatory for all school children, unless they have an exemption. Exemptions for personal and religious reasons have grown in the past decade. Geographic clustering of unvaccinated children in certain schools facilitates the spread of measles introductions, but the potential size, and thus risk, of outbreaks is unclear.
I will discuss our efforts to estimate potential outbreak sizes using an agent-based model, populated with a synthetic representation of the US state of Texas. Real schools are represented in the simulations and the current vaccination rate of each real school was applied to its in silico equivalent.

The talk is concerned with \emph{time-discretized} versions of the SIS (susceptible $\to$ infected $\to$ susceptible) epidemic model, which are derived by inspecting the number of infective hosts at a finite sequence of times $\tau_0=0<\tau_1<...<\tau_{m-1}<\tau_m=t'$, for a predetermined time $t'>0$ and an integer $m\in\mathbb{N}$. The aim is to construct a suitable criterion allowing us to summarize appropriately the dynamics of the number $I(t)$ of infective hosts over times $t\in[0,t']$ in terms of the number $\bar{I}_n=I(\tau_n+0)$ of infective hosts at equidistant times $\tau_n=n\tau$, for $n\in\{0,1,...,m\}$, with $\tau=m^{-1}t'$. Although it appears to be analytically intractable, the problem is closely related to the distribution of the total area between the sample paths of infectives in the continuous-time process ${\cal I}(t')=\{I(t): t\in [0,t']\}$ and its discrete-time counterpart $\bar{\cal I}^{(m)}=\{\bar{I}_n: n\in\{0,1,...,m\}\}$. Based on the effect of extreme values on the dynamics of ${\cal I}(t')$ and $\bar{\cal I}^{(m)}$, we conduct numerical results which show that, for any time interval of a predetermined length $t'>0$, it is generally possible to replace the SIS-model by a time-discretized version that is suitably selected by comparing the Hellinger distance between the corresponding extreme values distributions. We derive analytical expressions for key indexes --linked to the stationary numbers of infective hosts, the random length of an outbreak and the non-detection of an outbreak--, and we highlight the implications of their importance in the replacement of the original SIS-model by a certain time-discretized version. Our work complements to the work of Allen and Burgin ({\it Mathematical Biosciences}, {\bf 163,} (2000), 1--33), who define discrete-time SIS-models by assuming that at most one event (either an infection or a recovery) occurs in time steps of length $dt$, which is assumed to be sufficiently small.

Chemical reaction networks (CRNs) arise naturally as components of many physical and biological systems. Even when the elements of a system are not chemical in nature, the models which arise may be formally identical to CRN models. CRN theory focusses on making parameter-independent claims about CRNs. In other words, the goal is to describe behaviours of CRN models which arise as a consequence of the network structure and are largely independent of model details. The claims are generally about allowed or forbidden asymptotic behaviours. There are strands of work on conditions for multistationarity and oscillation; on the question of ”persistence”, namely whether some species can asymptotically ”run out” in a given CRN; on conditions for global stability of equilibria; and so forth. In many cases the results can naturally be implemented as algorithms, allowing for automated analysis of CRNs. The results from parameter-independent analysis form a natural precursor to more numerical and computational approaches needed for detailed analysis of CRN models.

Classical CRN theory focussed heavily on systems with mass action kinetics and gave rise to some powerful and useful theorems, particularly the deficiency zero and deficiency one theorems. In more recent times, the field has seen a resurgence of interest, with diverse mathematical tools being brought into play. This talk will outline some current themes in CRN theory, particularly focussed on how the presence or absence of particular subnetworks (”motifs”) influences allowed dynamical behaviours in ordinary differential equation models of CRNs. There are a number of results which take the form: ”a CRN containing no subnetworks of type X cannot display behaviour Y”. In the other direction we have results of the form: ”if a CRN contains a subnetwork of type X, then some model of this CRN admits behaviour Y”. The results are subtle and rely on appropriate notions of subnetwork, and assumptions about the class of kinetics. After a broad
introduction to the mathematical theory of CRNs, I’ll describe some of these results, and sketch some current challenges in this area.

There exists a toxic misfolded beta-sheet rich “scrapie” (PrPSc) isoform of Prion protein that induces misfolding in the healthy cellular form followed by fibril formation. Despite enormous efforts the structure of the scrapie remains elusive. Our goal is to use enhanced sampling techniques like Replica Exchange Molecular Dynamics (REMD) and metadynamics simulations to explore the complex conformational free energy landscape of Prion monomers and dimers to identify the structure of the scrapie form. Our study indicates that cellular form of Prion has a rather shallow free energy landscape with multiple low-lying metastable states that render the protein prone to misfolding. Also, we find that non-native hydrogen bonded interactions tend to stabilise these metastable states.

References:
• N. Chamachi and S. Chakrabarty, J. Phys. Chem. B 120, 7332 (2016)
• R. Singh, N. Chamachi, S. Chakrabarty and A. Mukherjee, J. Phys. Chem. B 121, 550 (2017)
• N. Chamachi and S. Chakrabarty, Biochemistry 56, 833 (2017)

The emergence of drug-resistant strains of M. tuberculosis poses a major threat to public health, warranting urgent attention to the problem of tackling antimicrobial resistance. A number of studies have sought to understand the causes of drug resistance, and have led to the identification of several mechanisms including mutations in key targets, upregulation of drug efflux pumps, etc. Yet, there is no understanding of which mechanisms are operative in a given condition, whether microbes explore multiple mechanisms simultaneously, or if such mechanisms are influenced by each other and lead to alterations in the cell in a synchronized manner. Towards this, an understanding of the global mechanisms leading to resistance becomes necessary. In this talk, I will describe different modelling approaches that we have adopted to address some of these questions and describe how we use them to identify strategic target combinations to tackle antimicrobial resistance.

Over the last years, a number of stochastic models have been proposed for analysing the spread of nosocomial infections in hospital settings. These models often account for a number of factors governing the spread dynamics: spontaneous patient colonization, patient-staff contamination/colonization, environmental contamination, patient cohorting, or healthcare workers (HCWs) hand-washing compliance levels. For each model, tailor-designed methods are implemented in order to analyse the dynamics of the nosocomial outbreak, usually by means of studying quantities of interest such as the reproduction number of each agent in the hospital ward, which is usually computed by means of stochastic simulations or deterministic approximations. In this work, we propose a highly versatile unified stochastic modelling framework that can account for all these factors simultaneously, and analyse the reproduction number of each agent at the hospital ward during a nosocomial outbreak, in an exact and analytical way. By means of five representative case studies, we show how this unified modelling framework comprehends, as particular cases, many of the existing models in the literature. We implement various numerical studies via which we: i) highlight the importance of maintaining high hand-hygiene compliance levels by HCWs, ii) support infection control strategies including to improve environmental cleaning during an outbreak, and iii) show the potential of some HCWs to act as super-spreaders during nosocomial outbreaks.

This work is based on the publication

L´opez-Garc´ıa M, Kypraios T (2018) A unified stochastic modelling framework for the spread of nosocomial infections.
Journal of the Royal Society Interface, 15: 20180060.

Micro-organisms are constantly monitoring their surrounding environment and making important lifestyle decisions. This decision process is governed by large genetic networks that process the information leading to a phenotypic response from the cell. Using the food-borne pathogen, Salmonella, as a model organism, I will discuss how cells encode strategies in networks to optimally control cellular behavior.

Salmonella, on ingestion with contaminated food, swims in small intestine using propeller-like structures, flagella, on its surface. On reaching the site of infection, it assembles a hypodermic needle on its surface using which it injects proteins into host cells. These proteins cause a change in the host-cell shape leading to internalization of the bacterium. If the bacterium fails to get internalized, it assembles finger-like projections, fimbriae, on its surface to adhere to and persist in the intestine. How Salmonella dynamically regulates gene expression and assembly of these organelles is the focus of this study. I will show that the networks controlling genes necessary for flagella, needle, and fimbriae are designed so as to encode logic gates and limit expression to conditions optimum for infection. In addition, there is cross-talk between these three systems which serves to dynamically control the timing of activation and de-activation of these networks. Collectively, cells dynamically process information in genetic networks which ensures that the encoded products are produced at the correct locales, at the appropriate levels, and for the appropriate amount of time

Modeling of viral dynamics has contributed to our understanding of the biology of multiple viruses. In particular, analyzing the kinetics of HIV-1 decay during antiretroviral therapy has elucidated details of viral infection, and parameters of virus and infected cell turnover, as well as the cell populations contributing to viral production. Antivirals from the integrase inhibitor class give rise to a pattern of HIV decay that is different from what had been observed before with other antiretrovirals. We modeled the effect of integrase inhibitors in short- and long-lived infected cells and fitted the model to data obtained from participants treated with different drug classes, including or not integrase inhibitors. This new model explains and quantifies the three phases of HIV-1 RNA decay with an integrase inhibitor vs. the two phases observed in therapies without it. In this way, the model provides a mechanistic description of viral infection that parsimoniously explains the kinetics of viral load decline under multiple classes of antiretrovirals.

Quantitative systems pharmacology (QSP) is a subset of pharmacometrics, which concerns the quantitative analysis of dynamic interactions between drugs and a biological system, with the aim to understanding the system as a whole. QSP models are often detailed mechanistic models, which have a large number of unknown parameters that have to be estimated from observed data. Since most biological processes are non-linear in nature, the identification of such highly parametrised non-linear models poses multiple challenges in the identification exercise. Sloppiness is one of the long discussed topics in the identification of biological processes. Sloppiness essentially quantifies anisotropy of model output to infinitesimal perturbations in the parameter space. Previous studies have shown that, for sloppy models, identification from data will result in extremely poor parameter estimates but reasonably good predictions. Sloppiness is placed somewhere in-between strict identifiability and loss of identifiability. Sloppiness seems to be closely connected to the concept of identifiability, but the exact relationship has hitherto not been elucidated. In this work, we have revisited the definition for sloppiness in the line of identifiability. We elucidate with simple toy examples, the exact roles of model structure, data and cost function in sloppiness and finally arrive at the necessary condition for sloppiness as the model structure. We have extended the concept of equality of model structures in discrete time systems to continuous time systems and delineated the difference between sloppiness and loss of identifiability due to data in the lens of predictions.

Prevention of pathogen transmission in hospital settings can be pursued by measures targeting a single pathogen (vertical intervention) or targeting more pathogens simultaneously (horizontal intervention).  Hand hygiene and universal cohorting of patients and health care workers (HCWs) are horizontal interventions, whereas cohorting of patients with known colonization, or improved hand hygiene by HCWs after contact with known colonized patients (isolation) are vertical interventions. We develop a stochastic modeling framework, based on the Master equation, to quantify the effects of different cohorting schemes, isolation and hand hygiene improvement on the prevalence of colonization with microorganisms in a small hospital unit with two types of HCWs, nurses (that can be cohorted) and physicians (that cannot be cohorted). Hand hygiene by HCWs is modeled as a chance of hand decontamination between two patient contacts. Hand hygiene adherence is assumed to be 43% for physicians and 59% for nurses and 31% of the patient contacts are due to physicians and 69% due to nurses.
We consider three cohorting schemes; (1) no cohorting (mass-action assumption); (2) 1^st-order cohorting (each patient has a preferred nurse and, if unavailable, other nurses are equally likely to provide care); and (3) higher-order cohorting 1^st-order cohorting incorporating also cohorting when first assigned nurses are not available) and we consider both horizontal and vertical cohorting and we vary the per admission reproduction number from 0.5 to 2 and the admission prevalence from 1% to 10%.
Hand hygiene improvement is more efficient than previous modeling studies suggest, as we take multiple failures in hand decontamination by HCWs in a row into account. When 80% of the contact of nurses are with patients in their own cohort, 1^st-order horizontal cohorting can reduce the number of acquisitions with 17% (R₀=0.5, admission prevalence f=0.1 to 34% for R₀=2 and f =0.01. In the absence of cohorting hand hygiene adherence of both nurses and physicians should improve by 16%, increasing the hand hygiene adherence from 0.59 to 0.66 for nurses and from 0.43 to 0.52 for physicians) and 18%, respectively, to realize the same prevalence reductions.  Higher-order cohorting can further augment effectiveness. The ultimate limiting factor are uncohorted physicians. Vertical cohorting is even more effective, and negative effects on the prevalence of pathogens for which vertical cohorting is not applied are very limited. A targeted hand hygiene improvement of 20%, either between patient contacts in different cohorts or after contact with isolated patients reduces the number of acquisitions with 14%-63% and 8%-37%.
We provide a general and flexible methodology to investigate the impact of transmission prevention measures. Our findings demonstrate that hand hygiene improvement, cohorting and isolation are powerful tools to prevent pathogen transmission in healthcare settings.
Given the well-known inverse relationship between workload of HCWs and hand hygiene compliance, our findings support more attention for staffing levels and cohorting structures as a measure to interrupt nosocomial transmission of pathogens.

Background: Tuberculosis (TB) continues to be the worlds greatest infectious diseases killer, with nearly 2million people per year dying from the disease. Many features of tuberculosis make it challenging to detect, understand and control including its long latent period, masked presentation particularly in children, and the heterogeneity of all aspects of the disease. Missing cases are a major reason TB is not well controlled today, as it is estimated that one in three cases of TB go undiagnosed.
Unlike many other diseases of major public health threat, HIV and malaria for example, TB is not well characterised in terms of infectiousness over the natural history of infection, and even in its latency period. Although different structures are used in modern TB models to simulate TB latency, it remains unclear whether they are all capable of reproducing the particular activation dynamics empirically observed. Statistical and mathematical models combined can be used to challenge the models with data and refine parameters to provide insights into disease dynamics and also potentially into the disease itself.
Aims: I will present work from my group on challenging model parameters with data specifically re-estimating the latent period of tuberculosis for different age groups and estimating death from tuberculosis by reanalysing the natural history data from the pre-chemotherapy era. I will then go on to show why getting these parameters matters from a disease control perspective.
Latency: We then fitted six different models (from the literature) to the activation dynamics observed from 1352 infected contacts diagnosed in low incidence countries (Australia and Netherlands) to obtain parameter estimates. Only models incorporating two latency compartments were capable of reproducing the activation dynamics empirically observed. Additionally, when two successive latency compartments are used, the first period should have a duration that is much shorter than that used in previous studies. Younger age categories showed a markedly higher early activation parameter. Models require at least two latency compartments and age-stratification in order to accurately replicate the dynamics of TB reactivation from latency. I will show why it is important to consider this in the fight against TB.
Mortality: Models of TB that use natural history parameters for mortality usually estimate death rates which are far in excess of those estimated by WHO and National TB control programs. The discrepancy is due to the death from cases missing from the national TB control program. It is difficult to reconcile data on mortality, missing cases and death rates from TB. I will present model results which suggest a large number of deaths from TB go unreported.

Tumor Necrosis Factor alpha (TNFα) is a pleiotropic cytokine involved in phenotypic decisions such as apoptotic/necrotic death, proliferation. Aberrant TNFα signaling is implicated in numerous pathological conditions such as neurological disorders, autoimmune diseases, cancer. Designing therapeutic strategies to modulate these conditions require insights into the mechanisms governing context-specific phenotypic response to TNFα. Signal transduction culminating in such responses is orchestrated by underlying molecular network of nodes (such as proteins, genes) interconnected by edges (such as protein-protein, protein-gene interactions). Deciphering mechanism(s) and identifying nodes/interactions controlling specific phenotypic response requires a holistic approach involving systematic analyses of the TNFα signaling network. In this talk, a combination of functionally consistent topological analysis and boolean dynamics simulations implemented on a well-annotated comprehensive TNFα signaling network to find targets for phenotype switching (from proliferation to apoptosis or vice-versa) will be presented. In particular, a graph-theory based network dimensionality reduction via modularization and the robustness properties will be used for finding potential target candidates. Systematic attractor analysis of the state transition graph of the network will be used for assessing the extent of phenotype switching that can be achieved when tese candidates are knocked-out.

The advent of single-cell RNA sequencing (scRNA-seq) technique has generated valuable resource on islet biology and type 2 diabetes (T2D). This provides an opportunity to understand the different cell types/states at both the network and individual gene expression levels. In this study, we inferred the gene regulatory networks (GRNs) of pancreatic cells from available scRNA-seq data in healthy and T2D using single-cell regulatory network inference and clustering workflow. Clustering of cells based on GRNs identifies endocrine and exocrine cells and multiple stable cell states in each alpha, beta and ductal cells. The phenotypic variations in cell states due to obesity and T2D are indistinguishable. Therefore, the trajectory of cells in pseudotime was constructed based on the cell-type-specific gene expression. The analysis shows that continuous spectrum of cell states exists with phenotypic-dependent branching and donor cell-cell variability in endocrine and exocrine cell types. We identified the genes that give rise to bifurcation in the trajectory. Our analysis demonstrates that the heterogeneity in pancreatic cells can be characterized at the network- and gene-level with the help of scRNA-Seq data.

Metastasis – the spread of cancer cells from one organ to another – causes above 90% of all cancer-related deaths. Despite extensive ongoing efforts in cancer genomics, no unique genetic or mutational signature has emerged for metastasis. However, a hallmark that has been observed in metastasis is adaptability or phenotypic plasticity – the ability of a cell to reversibly switch among different phenotypes in response to various internal or external stimuli. This talk will describe how mechanism-based mathematical models can help (a) identify how cancer cells can leverage this plasticity to drive cancer metastasis, (b) interpret confounding experimental and clinical data, and (c) guide the next set of crucial in vitro and in vivo experiments. Collectively, this work highlights how an iterative crosstalk between mathematical modeling and experiments can both generate novel insights into the emergent dynamics of cellular plasticity and uncover previously unknown accelerators of metastasis.

Surviving an infection or cancer often depends upon the extent and speed with which specific CD8+ T cells are amplified. It is not yet clear what drives the variation in the T cell response. We image the entire T cell response at single cell resolution to explore the contribution of each cell to the clonal response, with three major findings. First, the proliferation rate up to the fourth generation is tightly constrained, and does not contribute to clonal dominance. In contrast, divergence in cell cycle times and cell death from the fifth generation determines which clones will dominate. Second, characteristics of cell cycle and death are predominantly determined by the identity of the founder cell. Third, the size of the founder cell, prior to antigen presentation, is a strong predictor of the clonal response.

The key mechanisms of immune control of acute Zika virus infection are not fully understood, and furthering our knowledge of the within host dynamics of Zika virus will be important to the development of effective antiviral strategies. The majority of within host dynamics research has been performed in non-human primate (NHP) models of Zika infection, and understanding the role of inoculum dose is an important component in being able to translate results from a controlled experimental infection to a natural infection. Here we use mathematical modelling to analyze the within host dynamics of Zika virus in NHPs after infection at different inoculum doses. We find strong evidence for dose dependent innate immune control of plasma viral load.

Mathematical modellers have been able to fully characterize the replication kinetics of influenza A virus infections in vitro. These results have provided insight on the impact of a particular antiviral resistance mutation, and explained strain differences between avian and human influenza A virus. In their approach, the combination of a simple mathematical model and a key set of experiments was essential to the analysis. We discuss their approach, and apply a similar analysis to ebola virus infection in vitro for which preliminary results will be presented.

This hands-on section will provide an introduction to R (a language and environment for statistical computing), with specific applications to biological data analyses. We will start with an overview of this system, and its basic operations and data structures. We will build on these to showcase important features such as scripting of functions, statistical analyses and graphics. I will also present several interfaces and the power of packages.

It is expected that the students will have installed R and Rstudio on their computers, to work on practical examples.

Download R at https://cran.r-project.org/
Download RStudio at https://www.rstudio.com/

This hands-on section will provide an introduction to R (a language and environment for statistical computing), with specific applications to biological data analyses. We will start with an overview of this system, and its basic operations and data structures. We will build on these to showcase important features such as scripting of functions, statistical analyses and graphics. I will also present several interfaces and the power of packages.

It is expected that the students will have installed R and Rstudio on their computers, to work on practical examples.

Download R at https://cran.r-project.org/
Download RStudio at https://www.rstudio.com/

FRED (a Framework for Reconstructing Epidemiological Dynamics) is an agent-based model platform that uses synthetic populations that capture the demographic and geographically heterogeneous characteristics of actual populations, including neighborhood, household, school and workplace social networks. FRED populations are currently available for the United States and Telangana, India. FRED is a flexible system that can be used to model diverse situations, including infectious diseases, chronic conditions, demographic changes at the population level, and the effects of human behavior. FRED can be used to predict outcomes of an epidemic, such as epidemic curves and disease incidence, and is a tool for evaluating interventions, such as school closure, social distancing and changes in vaccination behavior.
Workshop participants will become familiar with the FRED platform, learning the basics of creating, running and analyzing agent-based simulations. The workshop will use FRED Web, an online interface to FRED. FRED Web is designed to facilitate model development and simulation, with a graphic user interface to guide model development.

FRED (a Framework for Reconstructing Epidemiological Dynamics) is an agent-based model platform that uses synthetic populations that capture the demographic and geographically heterogeneous characteristics of actual populations, including neighborhood, household, school and workplace social networks. FRED populations are currently available for the United States and Telangana, India. FRED is a flexible system that can be used to model diverse situations, including infectious diseases, chronic conditions, demographic changes at the population level, and the effects of human behavior. FRED can be used to predict outcomes of an epidemic, such as epidemic curves and disease incidence, and is a tool for evaluating interventions, such as school closure, social distancing and changes in vaccination behavior.
Workshop participants will become familiar with the FRED platform, learning the basics of creating, running and analyzing agent-based simulations. The workshop will use FRED Web, an online interface to FRED. FRED Web is designed to facilitate model development and simulation, with a graphic user interface to guide model development.

The need to acquire the skills to communicate one’s research to non-experts is being increasingly recognized by all stakeholders involved in research and development - funding agencies, journals, academic universities, as well as industries. Learning these skills is absolutely crucial today not only because interdisciplinary research where scientists trained in multiple disciplines collaborate based on tools and/or concepts is becoming the norm of the day, but also because many journals/granting agencies require authors to submit a ‘Significance Statement’ that should be understood by an ‘educated layman’.
By the end of this tutorial session that involves multiple interactive exercises such as improvisation and roleplaying, students will be able to:
1. Realize the jargon in the description of their research
2. Learn how to pitch their research in an engaging and exciting manner to a diverse audience
3. Consider the various need of a large audience

The need to acquire the skills to communicate one’s research to non-experts is being increasingly recognized by all stakeholders involved in research and development - funding agencies, journals, academic universities, as well as industries. Learning these skills is absolutely crucial today not only because interdisciplinary research where scientists trained in multiple disciplines collaborate based on tools and/or concepts is becoming the norm of the day, but also because many journals/granting agencies require authors to submit a ‘Significance Statement’ that should be understood by an ‘educated layman’.
By the end of this tutorial session that involves multiple interactive exercises such as improvisation and roleplaying, students will be able to:
1. Realize the jargon in the description of their research
2. Learn how to pitch their research in an engaging and exciting manner to a diverse audience
3. Consider the various need of a large audience

The need to acquire the skills to communicate one’s research to non-experts is being increasingly recognized by all stakeholders involved in research and development - funding agencies, journals, academic universities, as well as industries. Learning these skills is absolutely crucial today not only because interdisciplinary research where scientists trained in multiple disciplines collaborate based on tools and/or concepts is becoming the norm of the day, but also because many journals/granting agencies require authors to submit a ‘Significance Statement’ that should be understood by an ‘educated layman’.
By the end of this tutorial session that involves multiple interactive exercises such as improvisation and roleplaying, students will be able to:
1. Realize the jargon in the description of their research
2. Learn how to pitch their research in an engaging and exciting manner to a diverse audience
3. Consider the various need of a large audience

In this workshop, we introduce approaches to study biological populations using stochastic processes. Through deriving the Kolmogorov equations, we can form systems of ODEs that describe the time evolution of the transition probabilities, the probability of the stochastic process being in a particular state at a particular time. For some processes, analytic solutions to these equations can be obtained, however, when this is not possible the Kolmogorov equations can be manipulated to find expressions for generating functions and the mean population size. When models become too complex, analytical approaches are no longer feasible. In this case, we will introduce two simulations techniques, the Gillespie and tau-leaping algorithms, that allow us to create numerical realisations of the stochastic process in question. Once a stochastic model has been developed, we may wish to infer the parameters of our model from experimental data. We therefore introduce a Bayesian approach to do this that incorporates our prior beliefs about the parameters, along with the data, to produce a probability distribution for each parameter.

In this workshop, we introduce approaches to study biological populations using stochastic processes. Through deriving the Kolmogorov equations, we can form systems of ODEs that describe the time evolution of the transition probabilities, the probability of the stochastic process being in a particular state at a particular time. For some processes, analytic solutions to these equations can be obtained, however, when this is not possible the Kolmogorov equations can be manipulated to find expressions for generating functions and the mean population size. When models become too complex, analytical approaches are no longer feasible. In this case, we will introduce two simulations techniques, the Gillespie and tau-leaping algorithms, that allow us to create numerical realisations of the stochastic process in question. Once a stochastic model has been developed, we may wish to infer the parameters of our model from experimental data. We therefore introduce a Bayesian approach to do this that incorporates our prior beliefs about the parameters, along with the data, to produce a probability distribution for each parameter.

In this session, we will continue with the mathematical and computational approaches explained in TS4. The focus here will be on how some of the (approximative) numerical results obtained in TS4 by means of Gillespie simulations can be obtained analytically instead, in an exact way, by means of first-step arguments. We will show some applications in the area of mathematical epidemiology, moving from compartmental models for widely homogeneous populations to agent-based oriented approaches for more heterogeneous ones.