The intersection of the mathematical sciences with topics at the forefront of current biology is a rich source of mathematical problems. Quantifying biological phenomena through simple and more complex models, as well as achieving a deeper, more systematic understanding of these models, is a challenge that draws upon multiple skills. Interested mathematicians and scientists must draw upon very disparate aspects of mathematics. These include nonlinear dynamical systems, partial differential equations (such as the NavierStokes equations for fluids or the equations that govern biological pattern formation), information theory,stochastics and probability, network models and discrete mathematics relevant to computation.
This AIS is among the first of its kind in India to introduce a broad audience consisting of applied and pure mathematicians, physicists, engineers and some biologists to this active field. It provides a selection of topics that are among the forefront of those being studied internationally. It is aimed at those pursuing (or intending to pursue) research in any related area of mathematics (interpreted in a broad sense). A basic facility with di↵erential equations and some elementary probability will be assumed, but otherwise there are no prerequisites.
Speaker  No. of lectures  Syllabus 
I (KJ) Prof. Kavita Jain, JNCASR, Bengaluru 
6 
Mathematical Modelling in Population Biology: Lecture2 Mutation rates are also subject to the action of evolutionary forces. I will discuss some Lectures 3 & 4 will introduce some basic results in quantitative genetics and discuss how one can Tutorials1 & 2: 
II (MB) Prof. Malay Banerjee, IIT Kanpur 
6 
A survey of Ecological Models: Lecture2 Introduction to two species population models There are several types of population models of two interacting species  competitive, Tutorial1 Lecture3 Stability and bifurcation analysis for multispecies population models Mathematical models of interacting species with three and higher trophic levels can Lecture4 Spatiotemporal model  Turing instability Spatiotemporal models of interacting populations are capable to capture the effect of heterogeneous distribution of various species over their habitats on the resulting Tutorial2 
III (LN) Prof. Leelavati Narlikar, NCL, Pune 
6 
Sequence Analysis : Lecture1 Introduction to Algorithms and Probability Theory
Lecture2 Modeling biological sequences I
Lecture3 Modeling biological sequences II
Lecture4: Meta Genomics
Tutorial 1 
IV (GIM) Prof. Gautam I Menon, IMSc, Chennai 
6 
The Mathematics of Infectious Diseases: Lecture1 Introduction to the Modelling of Infectious Diseases This lecture provides the basic phenomena studied in infectious disease modelling, introduces the SI, SIR and more general compartmental models, and motivates the Lecture2 Host heterogeneities and multihost, multipathogen models Populations are heterogeneous and the generalisation of simple compartmental models to study such heterogeneities will be discussed. Several diseases can infect multiple Tutorial3 Implementing SIR and related models in simple computer programs Lecture4 Temporal Forcing and Stochastic Models Many diseases undergo forcing from some external factor, such as climate, rainfall or temperature. The basics of the modelling of forced systems will be described, as also the Lecture5 Spatial and Network models Spatial and network generalizations of the classic disease models, as well as their generalizations to agentbased models will be described. The basics of the Gillespie method will also be described. Tutorial6 Implementing agentbased models in simple computer models 
V (MT) Prof. Mukund Thattai, NCBS, Bengaluru 
6 
Models in Systems Biology: Lecture1 Gene regulatory networks. Models of transcriptional regulation

VI (MI) Prof. Mandar Inamdar, IIT Bombay 
6 
Mathematical Models for Continuous Media and Biological Applications : The broad scope of these lectures is to give the students basic understanding and implementable skill to model various phenomena in migration and mechanics of collective cell migration. To that end the lectures will be planned as follows. Each lecture/tutorial described below will be of 90 minutes duration. Lecture1 Introduction to continuum mechanics
Lecture2 Application of continuum modelling for biological tissues
Lecture3 Numerical techniques to solve continuum equations
Lecture4/Tutorial: Solve midlevel to simple problems in the three topics discussed above. Topics:
Lecture5 Discrete modelling of tissues and understanding the emergence of continuum level properties Topics:
Lecture6/Tutorial Handson implementation of mesoscale modelling involving coarsegraining of the vertex model to continuum level description Topic:

VII (PG) Prof. Pranay Goel, IISER Pune 
6 
Electrophysiological Models : Lecture1 Introduction to electrical phenomena in the nervous system . will introduce the basic biology of the nervous system; and the elementary ideas from circuit theory and their extensions that will be needed in later lectures. This will set the Lecture2 Modeling excitable media: The HodgkinHuxley equations of action potentials.We will develop the celebrated HodgkinHuxley model for electrical activity in nerves. We will then describe two broad classes of properties  Types I and II  that action potentials can be grouped into. Tutorial1 Introduction to XPP, and modelling excitable media. We will introduce XPP, a differential equations solutions package with a graphical interface. We will explore the HodgkinHuxley equations, and identify properties of Type I and II neurons using numerical experiments. Lecture3: Reduced models and phaseplane analysis of excitability. We will describe twodimensional models that successfully reproduce the essential properties of Type I and II neurons. We will carry out a phaseplane analysis to understand Lecture4 Modeling neural networks. will investigate synapses, and the connectivity of neurons in networks. We will introduce questions of emergent behaviours in neural networks, and briefly touch upon some methods that been used to investigate these phenomena. Tutorial 2 Neural networks. 
VIII (SS) Prof. Sitabhra Sinha, IMSc, Chennai 
6 
Networks Lecture1 Networks: An unifying framework for biology across scales Tutorial2 Identifying communities: Modularity, Graph partitioning and Synchronization & other collective dynamics in modular networks

Additional Resource persons
 Rahul Siddharthan (RS)
 Areejit Samal (AS)
 Sitabhra Sinha (SS)
The tutorials will be handled mostly by the lecturers with help from the resource persons listed above.
Timetable
Day  Date  Lecture 1 09:30–11:00 
Lecture 2 11:30–13:00 
Lecture 3 14:00 to 15:30 
Lecture 4 16:00–17:30 
1  3rd  I  II  III  IV 
2  4th  I  II  III  IV 
3  5th  I  II  III  IV 
4  6th  I  II  III  IV 
5  7th  I  II  III  IV 
6  8th  I  II  III  IV 
7  10th  V  VI  VII  VIII 
8  11th  V  VI  VII  VIII 
9  12st  V  VI  VII  VIII 
10  13nd  V  VI  VII  VIII 
11  14rd  V  VI  VII  VIII 
12  15th  V  VI  VII  VIII 