We consider a Kuramoto model of four-coupled oscillators of nonidentical initial frequencies. Under the influence of coupling, the oscillators fall into a full phase locked state of a common frequency when the coupling strength surpasses a threshold value. We find numerically the parameters that control this distinguishable coupling constant at the moment the oscillators transit into an entire frequency synchronization when a complete phase lock state takes place. We are able to set apart a recognizable phase condition at the fully locked state. This phase condition helps to derive an analytic formula to calculate the coupling factor as soon as the oscillators depart to a full phase locking state. The explicit expression of the edge coupling factor is given in terms of the initial frequencies of the four oscillators. The formula valid for calculating the distinct coupling allows to find mathematical expressions to calculate the phase differences when the four-coupled phase oscillators are strictly at the full phase locked state and have a common frequency synchronization.

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The present work aimed to study the effect of phenyl vinyl sulphone (PVS), a CPI, on different stages of Schistosoma (S.) mansoni in an in vitro culture study and in experimentally infected mice, compared to PZQ. As regards the in vitro study, different concentrations of PVS (1, 2, 4, 6, 8 and 10 µg/ml) and PZQ (1 µg/ml) were assessed by % worm mortality for schistosomula and adults, and hemoglobin degradation by schistosomula. In vivo study included 8 groups of mice. Intraperitoneal PVS, subgroup (a), and oral PZQ, subgroup (b), were assessed at different durations post infection (pi); at 1, 3, 5 and 7 weeks pi (groups I, II, III and IV, respectively). Infection, PVS, PZQ, and normal control groups (groups V-VIII) were included. The anti-schistosomal effects of PVS were assessed by parasitological, histopathological and haematological parameters. In in vitro study, PVS had a schistosomicidal effect in a concentration and time dependent manner, PVS showed 100% schistosomula mortality at day 2 and 92% adult worm mortality at day 5. Furthermore, PVS decreased hemoglobin degradation by schistosomula. In in vivo study, PVS showed a decrease in total worm burden and tissue egg load in intestine and liver with an increase in number of dead ova in intestine of mice. Furthermore, PVS resulted in a decrease in number, size and cellularity of hepatic granulomas and an increase in hemoglobin concentration.PVS was better than PZQ in reducing each of tissue egg count in intestine at 5 and 7 weeks pi, and hepatic granuloma size at 3, 5 and 7 weeks pi. These results suggest that PVS can be a promising chemotherapeutic agent in infection.