Time  Speaker  Title  Resources 

09:00 to 10:00    Registration & Welcome  
10:00 to 10:50  Jonathan Carruthers 
Stochastic dynamics of Francisella tularensis infection and replication 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 singlecell model we are able to approximate well the dynamics within the lung of an infected mice, comparing our results with those of agentbased 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 

10:50 to 11:20    Coffee break  
11:20 to 12:10  Sara Jabbari 
Novel strategies to tackle bacterial infections: targeting adhesion and persistence 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, reengineering 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 antivirulence 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 multidrug resistant bacterium Pseudomonas aeruginosa: targeting hostcell adhesion and cellmorphology transitions that facilitate persisterlike behaviour. Using mathematical modelling we consider ways to optimise the efficacy of such treatments. 

12:10 to 13:00  Rebecca Chisholm 
Understanding the relationship between the epidemiology of, and immune response to, Group A Streptococcus infection Group A Streptococcus (GAS) is a ubiquitous bacterial pathogen that exists in many distinct strains and is highly prevalent in Indigenous and other disadvantaged populations. It is responsible for a range of diseases – from superficial infections of the skin and throat, to lifethreatening invasive infections, and postinfection sequelae – and the relative prevalence of each of these diseases differ across populations. Vaccines against GAS are under development, but their effective use will require better understanding of how immunity develops following infection. In this presentation, I will discuss how we are using mathematical modelling in conjunction with local and global epidemiological data to gain insights into the withinhost infection and immunity dynamics of GAS. 

13:00 to 14:15    Lunch  
14:15 to 15:05  Sitabhra Sinha 
Games, Networks and Public Health: The source of disease prevalence information impacts effectiveness of vaccination programs The recent reports of dramatic increase in measles cases worldwide  particularly in the world’s most advanced economy, USA  is puzzling because an effective vaccine for the disease has existed for a long time. The answer seems to be that the very success of vaccination in reducing the burden of many diseases has paradoxically led to a decline in the number of people willing to get vaccinated. Thus, people think that they are now safe from an epidemic and can avoid getting vaccinated themselves (or their children). Can apparently rational decisions by individuals, viz. not to vaccinate, potentially lead to a catastrophic consequences for society, viz., opening it upto deadly epidemics ? In this talk we show how the decision of individuals to vaccinate themselves is influenced by their risk perception regarding contracting the disease, which in turn in based on information they have about epidemic incidence and the fraction of neighbors on their social network who are protected through vaccination. Using a game theoretic framework we show that optimal public health outcomes arise when individuals use information about disease prevalence in the local neighborhood of their social network, in contrast to relying on global prevalence information obtained from mass media. Our results strongly suggests the need for a transparent system of disseminating detailed incidence information about an ongoing epidemic to the public, such that individuals can make informed vaccination decisions based on realtime data for their neighborhood. This is a collaboration with Dr Anupama Sharma (IMSc Chennai), Dr Shakti N Menon (IMSc Chennai) and Dr V Sasidevan (IMSc Chennai & CUSAT Cochin). Reference: 

15:05 to 15:55  David R Sinclair 
Expected size of measles outbreaks caused by vaccination exemptions for school children 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. 

15:55 to 16:25    Coffee break  
16:25 to 17:15  Antonio Gómez Corral 
A comparative analysis between two timediscretized versions of the SIS epidemic model The talk is concerned with \emph{timediscretized} 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 $\tau_0=0<\tau_1<...<\tau_{m1}<\tau_m=t'$, 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 continuoustime process ${\cal I}(t')=\{I(t): t\in [0,t']\}$ and its discretetime 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 SISmodel by a timediscretized 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 nondetection of an outbreak, and we highlight the implications of their importance in the replacement of the original SISmodel by a certain timediscretized version. Our work complements to the work of Allen and Burgin ({\it Mathematical Biosciences}, {\bf 163,} (2000), 133), who define discretetime SISmodels 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. 

17:15 to 17:40  Ravishankar. N 
Statistical modelling of Dengue incidences and climatic variables in India This talk focuses on “Dengue”, which is considered as a one of the major public health threats in India. It aims to model the yearly state wise dengue incidences with respect to selected climatic variables namely annual rainfall and average temperature from the year 2008 to 2017 and identify hotspots of dengue incidence in states of India. Data required for the study were collected from www.indiastat.com. The expected dengue incidences were modelled using negative binomial regression with states as random effect and covariates as climatic variables and year. To identify the spatial clustering of dengue incidences, appropriate spatial clustering algorithm was used. To assess the spatial clustering of dengue incidences, Local Indicator of Spatial Association (LISA) was used. The hot spots for dengue incidence in states of India were determined using GeoDa/SatScan. From the study it was found that there is no association between the dengue incidences and climatic variables  average temperature and annual rainfall in India. Karnataka, Kerala and Tamilnadu were found to be the hotspots of dengue incidences 
Time  Speaker  Title  Resources 

09:00 to 10:00    Discussions and Collaborations  
10:00 to 11:00  Carmen MolinaParís  Adventures in mathematical immunology  
11:00 to 11:30    Coffee break  
11:30 to 12:30  Ruy Ribeiro 
Introduction to data analyses with R (Tutorial Session 1) This handson 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.rproject.org/ 

12:30 to 13:30    Lunch  
13:30 to 14:30  Ruy Ribeiro 
Introduction to data analyses with R (Tutorial Session 1) This handson 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.rproject.org/ 

14:30 to 15:30  Ruy Ribeiro 
Introduction to data analyses with R (Tutorial Session 1) This handson 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.rproject.org/ 

15:30 to 16:00    Coffee break  
16:00 to 17:00  Ruy Ribeiro 
Introduction to data analyses with R (Tutorial Session 1) This handson 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.rproject.org/ 
Time  Speaker  Title  Resources 

09:00 to 10:00  Mohit Kumar Jolly 
Communicating science to nonexperts (Tutorial Session 3) The need to acquire the skills to communicate one’s research to nonexperts 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’. 

10:00 to 11:00  Mohit Kumar Jolly 
Communicating science to nonexperts (Tutorial Session 3) The need to acquire the skills to communicate one’s research to nonexperts 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’. 

11:00 to 11:30    Coffee break  
11:30 to 12:30  Mohit Kumar Jolly 
Communicating science to nonexperts (Tutorial Session 3) The need to acquire the skills to communicate one’s research to nonexperts 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’. 

12:30 to 13:30    Lunch  
13:30 to 14:30  Mohit Kumar Jolly 
Communicating science to nonexperts (Tutorial Session 3) The need to acquire the skills to communicate one’s research to nonexperts 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’. 

14:30 to 15:30  Jonathan Carruthers 
Stochastic modelling of processes in Biology I (Tutorial Session 4) 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 tauleaping 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. 

15:30 to 16:00    Coffee break  
16:00 to 17:00  Jonathan Carruthers 
Stochastic modelling of processes in Biology I (Tutorial Session 4) 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 tauleaping 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. 
Time  Speaker  Title  Resources 

09:00 to 10:00    Discussions and Collaborations  
10:00 to 11:00  Jonathan Carruthers 
Stochastic modelling of processes in Biology I (Tutorial Session 4) 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 tauleaping 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. 

11:00 to 11:30    Coffee break  
11:30 to 12:30  Jonathan Carruthers 
Stochastic modelling of processes in Biology I (Tutorial Session 4) 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 tauleaping 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. 

12:30 to 13:30    Lunch  
13:30 to 14:30  Martín LópezGarcía 
Stochastic modelling of processes in Biology II (Tutorial Session 5) 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 firststep arguments. We will show some applications in the area of mathematical epidemiology, moving from compartmental models for widely homogeneous populations to agentbased oriented approaches for more heterogeneous ones. 

14:30 to 15:30  Martín LópezGarcía 
Stochastic modelling of processes in Biology II (Tutorial Session 5) 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 firststep arguments. We will show some applications in the area of mathematical epidemiology, moving from compartmental models for widely homogeneous populations to agentbased oriented approaches for more heterogeneous ones. 