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Modelling infectious diseases


Unit 1. Introduction to Mathematical modeling: ODEs, System of ODEs and their numerical solution, stability analysis.

 Disease and mathematical models: type of diseases, characterization of diseases, control of infectious diseases, mathematical models (what they can do, their limitations); 

Unit 2. Concepts of mathematical modelling of infectious diseases;  Simple epidemic models, formulating deterministic Susceptible-infected (SI) models, Susceptible-infected-recovered (SIR) model, SIR model without demography (threshold, epidemic burnout), SIR model with demography (equilibrium state, stability properties, oscillatory dynamics, sensitivity analysis, mean age, ...), without immunity, waning immunity (SIRS) model, adding a latent period and Susceptible-Exposed-Infected-Recovered (SEIR) model,  Infections with a carrier state;  Discrete-time models; 

Unit 3. Parameterization (estimating risk of infection R0, size of an epidemic, from reported cases, seroprevalence data, estimating parameters in general, disease free equilibrium, stability analysis). 

Unit 4. Models for describing STI and HIV transmission and control; Analyses of serological data: methods for estimating age and time-dependent transmission rates and their application for developing models of the dynamics of infections; Models of the dynamics and control of vector-borne diseases, tuberculosis; Spatial models (concepts of heterogeneity, interaction, isolation, localized extinction, metapopulations, lattice-based models, individual based models).

Unit 5. Stochastic modeling of infectious diseases and Networks, Model choice