Optimizing hospital distribution across districts to reduce tuberculosis fatalities.

The spatial distributions of diverse facilities are often understood in terms of the optimization of the commute distance or the economic profit. Incorporating more general objective functions into such optimization framework may be useful, helping the policy decisions to meet various social and economic demands. As an example, we consider how hospitals should be distributed to minimize the total fatalities of tuberculosis (TB). The empirical data of Korea shows that the fatality rate of TB in a district decreases with the areal density of hospitals, implying their correlation and the possibility of reducing the nationwide fatalities by adjusting the hospital distribution across districts. Approximating the fatality rate by the probability of a patient not to visit a hospital in her/his residential district for the duration period of TB and evaluating the latter probability in the random-walk framework, we obtain the fatality rate as an exponential function of the hospital density with a characteristic constant related to each district's effective lattice constant estimable empirically. This leads us to the optimal hospital distribution which finds the hospital density in a district to be a logarithmic function of the rescaled patient density. The total fatalities is reduced by 13% with this optimum. The current hospital density deviates from the optimized one in different manners from district to district, which is analyzed in the proposed model framework. The assumptions and limitations of our study are also discussed.

Self-attracting walk on heterogeneous networks.

Understanding human mobility in cyberspace becomes increasingly important in this information era. While human mobility, memory-dependent and subdiffusive, is well understood in Euclidean space, it remains elusive in random heterogeneous networks like the World Wide Web. Here we study the diffusion characteristics of self-attracting walks, in which a walker is more likely to move to the locations visited previously than to unvisited ones, on scale-free networks. Under strong attraction, the number of distinct visited nodes grows linearly in time with larger coefficients in more heterogeneous networks. More interestingly, crossovers to sublinear growths occur in strongly heterogeneous networks. To understand these phenomena, we investigate the characteristic volumes and topology of the cluster of visited nodes and find that the reinforced attraction to hubs results in expediting exploration first but delaying later, as characterized by the scaling exponents that we derive. Our findings and analysis method can be useful for understanding various diffusion processes mediated by human.