Long-range correlations improve understanding of the influence of network structure on contact dynamics.

Models of infectious diseases are characterized by a phase transition between extinction and persistence. A challenge in contemporary epidemiology is to understand how the geometry of a host's interaction network influences disease dynamics close to the critical point of such a transition. Here we address this challenge with the help of moment closures. Traditional moment closures, however, do not provide satisfactory predictions close to such critical points. We therefore introduce a new method for incorporating longer-range correlations into existing closures. Our method is technically simple, remains computationally tractable and significantly improves the approximation's performance. Our extended closures thus provide an innovative tool for quantifying the influence of interaction networks on spatially or socially structured disease dynamics. In particular, we examine the effects of a network's clustering coefficient, as well as of new geometrical measures, such as a network's square clustering coefficients. We compare the relative performance of different closures from the literature, with or without our long-range extension. In this way, we demonstrate that the normalized version of the Bethe approximation-extended to incorporate long-range correlations according to our method-is an especially good candidate for studying influences of network structure. Our numerical results highlight the importance of the clustering coefficient and the square clustering coefficient for predicting disease dynamics at low and intermediate values of transmission rate, and demonstrate the significance of path redundancy for disease persistence.

In vivo activity and pharmacodynamics of amoxicillin in combination with fosfomycin in fibrin clots infected with highly penicillin-resistant Streptococcus pneumoniae.

Using a clinical pneumococcal strain for which MICs were 4, 2, and 32 mg/liter for penicillin, amoxicillin, and fosfomycin, respectively, we studied the efficacies of these antibiotics alone and their combinations in the treatment of prolonged (48-h) experimental fibrin clot infection in rabbits. Treatments were as follows: amoxicillin IV at 20 mg/kg of body weight in one dose (Amo20), 50 mg/kg in one dose (Amo50), or two doses 6 h apart (Amo20 x 2 and Amo50 x 2); fosfomycin IV at a fixed dose of 50 mg/kg in one dose (Fos50) or two divided doses 6 h apart (Fos50 x 2); or the combinations of amoxicillin and fosfomycin with the same schedules. Maximum concentrations in clots were 2.03 +/- 1.02 and 2.13 +/- 0.33 mg/liter for Amo20 regimens, 3.7 +/- 1.9 and 4 +/- 1.3 mg/liter for Amo50 regimens, and 24 +/- 7 and 40 +/- 8 mg/liter for fosfomycin regimens, respectively. The mean half-lives of elimination from clots were between 2 and 3 h for amoxicillin regimens and between 5 and 7 h for fosfomycin. We observed the highest bacterial reductions (log10 CFU/gram) for Amo50 in two divided doses with or without fosfomycin. A significantly higher bacterial reduction than that with each monotherapy was observed when Amo20 was combined with fosfomycin in either one dose or two doses 6 h apart (0.16 +/- 0.8 and 1.64 +/- 1.6 log10 CFU/g for Amo20 in one and two doses, respectively, and 0.93 +/- 0.81 and 0.61 +/- 0.56 log10 CFU/g for fosfomycin in one and two doses, respectively, versus 3.46 +/- 1.26 and 3.16 +/- 1.31 log10 CFU/g for Amo20 plus fosfomycin in one and two doses, respectively [P < 0.001]). A time-dependent effect was observed with amoxicillin regimens. The time of regrowth was significantly delayed when amoxicillin was combined with fosfomycin. By using a multivariate analysis, we demonstrated that the most important parameter correlated to efficacy of the combination amoxicillin-fosfomycin was the length of the period during which the concentration of amoxicillin remained above the MIC. We demonstrated that the in vivo efficacy of the combination of amoxicillin and fosfomycin gave higher antibacterial effect than each monotherapy.