The course aims at providing students the basis of matematical modeling applied to Biology, both from a theoretical point of view via differential equations of various kinds, and from the numerical and computational point of view in order to simulate their solutions. The course is also meant to enable students catching the usefulness of and the criticism in the use of mathematical modelling in Life Sciences in order to describe complex phenomena and predict possible scenarios.

1. The basis of mathematical modeling

1.1 What is a mathematical model?

1.2 Characteristics of a mathematical model

2. Differential Equations and Differential Systems

2.1 Background to the concepts of derivative and integral of a function.

2.2. Ordinary Differential Equations and Cauchy problem (ODEs).

2.3 (Hints on) Delay Differential Equations (DDEs).

2.4 Stochastic Differential Equations (SDEs).

3. Differential modeling of biological processes

3.1 Models for popuation growth: Malthus, Verhulst, Gompertz.

3.2 Models for the spread of infections; SI, SIS, SIR, SI(R)S, SEIR. Applications to Covid-19.

3.3 Modeling bacteria-bacteriophage infections in marine environment (ODEs, SDEs).

3.4 The use of MATLAB for the simulation of the solutions of models introduced in 3.1 - 3.2.

Although not mandatory, having passed the exam of Mathematics is strongly recommended.

Students should demonstrate:

D1. Thorough knowledge and non mnemonic comprehension of the treated issues.

D2. Capability of application of the concepts of derivative and integral of a mathematical function to modeling.

D3. Capability of justifying each equation in a model according to its biological meaning 

D4. Capability of defending a thesis, making links among different studied issues, enhancing strength and weakness points of a mathematical model applied to Biology.

D5. Ability of using a rigorous scientific language in the exposition of the studied issues.

The teaching material prepared by the lecturer in addition to recommended textbooks (such as for instance slides, lecture notes, exercises, bibliography) and communications from the lecturer specific to the course can be found inside the Moodle platform › blended.uniurb.it

None

Teaching

- Frontal lessons

- Regular check of uploaded material on the Moodle platform 

Attendance

Not mandatory

Course books

Uploaded material on the Moodle platform; slides, scientific papers and useful links. 

Assessment

Oral examination consisting in:

1) introduction and discussion of numerical results of one of the differential models studied during the academic year or a new one according to the student's choice. In this second case, the student HAS TO SEND TO THE TEACHER (margherita.carletti@uniurb.it), NOT LATER THAN 5 DAYS BEFORE THE EXAMINATION DAY, one or more scientific articles and/or other material useful to understand the biological problem and evaluate the student's presentation.

The maximun available time to the student for his/her discussion of the chosen model is 30 minutes.

Disability and Specific Learning Disorders (SLD)

Students who have registered their disability certification or SLD certification with the Inclusion and Right to Study Office can request to use conceptual maps (for keywords) during exams.

To this end, it is necessary to send the maps, two weeks before the exam date, to the course instructor, who will verify their compliance with the university guidelines and may request modifications.

Teaching

Regular check on the Moodle platform.

Attendance

Not mandatory

Course books

Uploaded material on the Moodle platform; slides, scientific papers and useful links. 

Assessment

Same as ATTENDING STUDENTS.

Disability and Specific Learning Disorders (SLD)

Students who have registered their disability certification or SLD certification with the Inclusion and Right to Study Office can request to use conceptual maps (for keywords) during exams.

To this end, it is necessary to send the maps, two weeks before the exam date, to the course instructor, who will verify their compliance with the university guidelines and may request modifications.