Kalman filtering approach for early estimation of the number of hidden HIV infected patients

In any epidemic spread there is a group of individuals strongly involved in the diffusion of the infection but without any evidence of infectiousness, like during incubation periods. It is important to estimate this number, in order to adequately allocate resources to face the possible forthcoming epidemic emergency. This is the problem faced in this paper referring to the HIV-AIDS epidemic; this sanitary emergency is peculiar for the long incubation time: it can reach even 10 years, a long period in which the individual can unconsciously infect other subjects. The identification of the number of infected subjects is here obtained by using the extended Kalman filter applied to a noisy model in which only the number of infected diagnosed patients is available. Numerical simulations support the effectiveness of the approach.