Numerical simulation of agent-based model describing human migration

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HTLV-I is a retrovirus that causes ATL. The transmission routes of HTLV-I are (i) from infected mothers to their new born babies, (ii) from infected males (husbands) to females (their wives) by long-term sexual intercourse, and (iii) from infected females (wives) to males (their husbands). In the first paper of the references we consider the population dynamics of HTLV-I infection in a discrete-time mathematical model incorporating an age structure. The necessary and sufficient condition for the extinction of HTLV-I is derived from the model. In order to quantitatively describe interregional migration, in the second paper of the references, we construct two stochastic agent-based models that consist of a large number of agents relocating to obtain higher utility in a discrete bounded domain. In one model we assume that the utility is defined as an increasing affine function of the density of agents. In the other model we assume that the utility is equal to a concave quadratic function of the density of agents. We obtain estimates for the behavior of the models when the number of agents and the time variable tend to infinity. In the third paper of the references we mathematically prove that if the effort required in moving is large, then the models are close to each other in the following sense : the mixed problem with the periodic boundary condition for the master equation has a unique solution that is very close to a solution of that for the Fokker-Planck equation, where the effort is a sociodynamic quantity that represents a cost incurred in moving.