Koji Sugiura, Yukio Sakisaka, Nariyuki Nakagiri, Jin Yoshimura, Kei-ichi Tainaka
In Anderssen, R.S., R.D. Braddock and L.T.H. Newham (eds) 18th World IMACS Congress and MODSIM09 International Congress on Modelling and Simulation., 197-203, Jul, 2009 Peer-reviewed
The spatial and temporal dynamics for epidemic diseases have growing interest. A variety of theoretical models have been presented by many authors. Examples are SIR, SIS, SIRS models. By the use of these models, both effects of prevention and quarantine have been explored for the suppression of disease. Here, the term "prevention" denotes that the susceptible person behaves not to be infected; examples are vaccination and preventable behaviors. In contrast, we use the term "quarantine" as the decrease of infection opportunity; if people avoid the interactions, the infection will be reduced. In the present paper, we study the SIS model on a square lattice: It is called "contact process" or "lattice logistic model." The contact process has been extensively investigated by many fields, such as mathematics, physics and ecology. Each lattice site takes one of three states: susceptible (S), infected (I) and prevention (P) sites. Infection is assumed to occur between S and I at adjacent sites: no infection occurs for P. To explore both effects of prevention and quarantine, we apply the site and bond percolations respectively. Computer simulations reveal that the system evolves into an equilibrium state. When the infection rate beta increases, or when the recovering rate gamma decreases, then the equilibrium density of I increases. The final equilibrium state becomes either infectious or disease-free phase. The boundary between both phases can be represented by a scaling law. The mean-field theory well predicts such infection dynamics and the scaling law. However, the theory never predicts the following "percolation thresholds": When both levels of prevention and quarantine exceed a threshold (percolation threshold), the disease is effectively suppressed irrespective of the values of beta and gamma. The percolation means the spatial connection of protected people which cooperatively prohibits the infection.