Kinetic model for wealth distribution in presence of epidemic dynamics with asymptomatic cases

The aim of the thesis is to combine kinetic theory for wealth distribution with a model for the spread of epidemics so that we can study the economic impact of infectious disease such as the one caused by the COVID-19 virus. In detail we choose to use a SIAR system, i.e. a model that takes into account four different compartment classes of individuals: Susceptible, Infected, Asymptomatic and Recovered. It turns out to be the best compromise between a better accuracy than classical SIR model, and the possibility to make a system of kinetic equations not too complex. Indeed we transform the system of ODEs into one of PDEs not explicitly resolvable but that we can study, although with some simplifications, both analytically and numerically, finding a steady state for the wealth distribution functions of each class. So we start by defining the binary interaction rules and then we obtain suitable Boltzmann-type equations for each group of individuals. Analytically we resort to the so-called quasi-invariant scaling of exchange to get Fokker-Planck equations whose equilibrium is often computable analytically. Therefore we analyse various scenarios and see how different types of interactions modify the Gini coefficient of the stationary solution. From the numerical point of view, we adopted suitable Monte Carlo methods for the Boltzmann equation.