Using lattice SIS epidemiological model with clustered treatment to investigate epidemic control

In epidemic control, how the size of treatment blocks influences the disease is a very interesting problem. Here, we construct an SIS model with spatially clustered treatment blocks using cellular automata and pair approximation to investigate the disease control and optimal arrangement of treatment blocks. On a same treatment intensity, the treatment blocks are built randomly and the individuals in the treatment blocks are cured in the next interval. The migration and neighboring structures are also considered in this model. We find that the size of treatment blocks will influence the control of disease. The bigger size of treatment blocks is more effective in epidemic control. The results obtained by lattice simulations and pair approximation respectively are consistent. On the same treatment arrange, higher migration rate has completely different influence on the epidemic depending on different neighboring structures. Besides, in different neighboring structures, both infected and susceptible populations will get clustered under the treatment blocks. Meanwhile, the neighboring structures can influence the degree of aggregation and the bigger treatment blocks can promote the aggregation compared to the smaller ones. The results here are significant for the control of epidemic diseases, especially when available medical resources are limited.