Mathematical Modeling in Evolutionary and Environmental Biology
A.Y. 2018/2019
Learning objectives
* Apprendere ad utilizzare semplici modelli matematici per approfondire la comprensione qualitativa e quantitativa di fenomeni biologici.
* Studiare semplici modelli per la dinamica di popolazioni e di infezioni epidemiche.
* Studiare l'aspetto quantitativo della teoria dell'evoluzione
* Apprendere strumenti matematici di utilizzo generale nelle scienze quali equazioni differenziali, ed il concetto di stabilita' delle soluzioni.
* Studiare semplici modelli per la dinamica di popolazioni e di infezioni epidemiche.
* Studiare l'aspetto quantitativo della teoria dell'evoluzione
* Apprendere strumenti matematici di utilizzo generale nelle scienze quali equazioni differenziali, ed il concetto di stabilita' delle soluzioni.
Expected learning outcomes
Undefined
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Course syllabus
· Linear discrete time dynamics: Fibonacci, models with delay, higher dimensional Malthus models, matrices, eigenvectors and eigenvalues.
· Nonlinear discrete time dynamics: equilibria, stability and instability, caos in the logistic model. Overcompensation ed undercompensation. The works of May and Hassel.
· Continuous time dynamics: equilibria. Stability and instability. Linearization.
· Modeling population growth. Exponential growth, logistic growth and other size dependent models.
· Other biological applications of exponential and logistic growth. Holiing's type functional response.
· Interacting populations in discrete time: parassitoidism.
· Interacting populations: predation and cooperation. Lotka-Volterra model and D'Ancona paradox.
· Infection and epidemiological models: SIR model and vaccination.
· Interacting polulations: competition. The principle of competitive exclusion.
· Mathematical theory of evolution: introduction (fitness frequency in the model at constant fitnesses, Fisher Theorem, games theory and cooperation/competition, stability under invasion, mutation in a 2-states model).
Reference Material
*G. Gaeta, Modelli Matematici in Biologia; Springer 2007
*Mathematical Models in Biology - (Leah Edelstein-Keshet)
*Mathematical Epidemiology - Lecture Notes in Mathematics - (Fred Brauer, Pauline van den Driessche and Jianhong Wu)
*Mathematical Models in Population Biology and Epidemiology - Texts in Applied Mathematics (Fred Brauer and Carlos Castillo-Chavez)
Prerequisites and exam evaluation
We assume the student to be acquainted with the tools and ideas of a first course in calculus: theory of single real variable functions, derivatives and integrals, introduction to probability and linear algebra (matrices, vectors, determinants).
Examination procedure: it consists in a written test, whose duration is about 150 minutes, during which the student is asked to develop and solve 3 o 4 exercises. Techniques needed to face the assigned exercises are developed and carefully explained during the lectures. For such a reason, attendance is strongly recommended.
Language of instruction
Italian
WEB Page
http://www.mat.unimi.it/users/penati/Biomat.html
· Nonlinear discrete time dynamics: equilibria, stability and instability, caos in the logistic model. Overcompensation ed undercompensation. The works of May and Hassel.
· Continuous time dynamics: equilibria. Stability and instability. Linearization.
· Modeling population growth. Exponential growth, logistic growth and other size dependent models.
· Other biological applications of exponential and logistic growth. Holiing's type functional response.
· Interacting populations in discrete time: parassitoidism.
· Interacting populations: predation and cooperation. Lotka-Volterra model and D'Ancona paradox.
· Infection and epidemiological models: SIR model and vaccination.
· Interacting polulations: competition. The principle of competitive exclusion.
· Mathematical theory of evolution: introduction (fitness frequency in the model at constant fitnesses, Fisher Theorem, games theory and cooperation/competition, stability under invasion, mutation in a 2-states model).
Reference Material
*G. Gaeta, Modelli Matematici in Biologia; Springer 2007
*Mathematical Models in Biology - (Leah Edelstein-Keshet)
*Mathematical Epidemiology - Lecture Notes in Mathematics - (Fred Brauer, Pauline van den Driessche and Jianhong Wu)
*Mathematical Models in Population Biology and Epidemiology - Texts in Applied Mathematics (Fred Brauer and Carlos Castillo-Chavez)
Prerequisites and exam evaluation
We assume the student to be acquainted with the tools and ideas of a first course in calculus: theory of single real variable functions, derivatives and integrals, introduction to probability and linear algebra (matrices, vectors, determinants).
Examination procedure: it consists in a written test, whose duration is about 150 minutes, during which the student is asked to develop and solve 3 o 4 exercises. Techniques needed to face the assigned exercises are developed and carefully explained during the lectures. For such a reason, attendance is strongly recommended.
Language of instruction
Italian
WEB Page
http://www.mat.unimi.it/users/penati/Biomat.html
Professor(s)
Reception:
to be fixed by email
office num. 1039, first floor, Dep. Mathematics, via Saldini 50