ABSTRACT
In recent years, the epidemic model with anomalous diffusion has gained popularity in the literature. However, when introducing anomalous diffusion into epidemic models, they frequently lack physical explanation, in contrast to the traditional reaction-diffusion epidemic models. The point of this paper is to guarantee that anomalous diffusion systems on infectious disease spreading remain physically reasonable. Specifically, based on the continuous-time random walk (CTRW), starting from two stochastic processes of the waiting time and the step length, time-fractional space-fractional diffusion, time-fractional reaction-diffusion and fractional-order diffusion can all be naturally introduced into the SIR (S: susceptible, I: infectious and R: recovered) epidemic models, respectively. The three models mentioned above can also be applied to create SIR epidemic models with generalized distributed time delays. Distributed time delay systems can also be reduced to existing models, such as the standard SIR model, the fractional infectivity model and others, within the proper bounds. Meanwhile, as an application of the above stochastic modeling method, the physical meaning of anomalous diffusion is also considered by taking the SEIR (E: exposed) epidemic model as an example. Similar methods can be used to build other types of epidemic models, including SIVRS (V: vaccine), SIQRS (Q: quarantined) and others. Finally, this paper describes the transmission of infectious disease in space using the real data of COVID-19.
ABSTRACT
One of the most effective strategies to mitigate the global spreading of a pandemic (e.g. coronavirus disease 2019) is to shut down international airports. From a network theory perspective, this is since international airports and flights, essentially playing the roles of bridge nodes and bridge links between countries as individual communities, dominate the epidemic spreading characteristics in the whole multi-community system. Among all epidemic characteristics, the peak fraction of infected, I-ma(x), is a decisive factor in evaluating an epidemic strategy given limited capacity of medical resources but is seldom considered in multi-community models. In this article, we study a general two-community system interconnected by a fraction r of bridge nodes and its dynamic properties, especially I-max, under the evolution of the susceptibleinfected-recovered model. Comparing the characteristic time scales of different parts of the system allows us to analytically derive the asymptotic behaviour of I-max with r, as r -> 0, which follows different power-law relations in each regime of the phase diagram. We also detect crossovers when I-max changes from one power law to another, crossing different power-law regimes as driven by r. Our results enable a better prediction of the effectiveness of strategies acting on bridge nodes, denoted by the power-law exponent epsilon(I) as in I-max proportional to r(1/epsilon I).
ABSTRACT
OBJECTIVE: During the epidemic period of COVID-19, the treatment of breast cancer patients is limited to a great extent. Their psychological changes deserve attention. The purpose of this study was to investigate the psychological health, anxiety and depression of breast cancer patients during COVID-19. Compare them with healthy people in the same period, so as to lay a foundation for psychological intervention of breast cancer before and after the COVID-19 outbreak. METHODS: During 2019-01-10 and 2020-01-13, 128 female breast cancer patients in the First(86 cases) and Second(42 cases) Affiliated Hospitals of the Air Force Military Medical University were selected as the study objects (group A), and 121 social healthy adult women randomly answered by the Internet questionnaire were selected as the control group (group B). SCL-90, SAS and SDS were used to complete the questionnaire survey. RESULTS: The positive results of SCL-90 were as follows: anxiety(21.09%) and depression(17.18%) were the most common in group A;Anxiety(14.88%) and hostility(15.7%) were the most common in group B. Factor score analysis showed that depression(t=2.898, P=0.004), anxiety(t=3. 649, P<0.001) and hostility(t=3.824, P<0.001) in group A were higher than those in group B. The depression and anxiety of group B were higher than that of domestic norm. Further SAS and SDS analysis showed that anxiety(t=11.492, P<0.001) and depression(t=10.871, P<0.001) in group A were significantly higher than those in group B. In each subgroup: The psychological problems of depression(t=2.061, P=0.044), anxiety(t=2.183, P=0.039) and hostility(t=2.028, P=0.048) of patients who were under 45 years were more obvious than those patients who were over 45 years. The psychological problems of depression(t=2.759, P=0.007), anxiety(t=2.348, P=0.018) and fear(t=2.182, P=0.043) of the patients without higher education were more obvious than those of the educated. The psychological problems of depression(t=2.064, P=0.043), anxiety(t=2.581, P=0.017) and fear(t=2.086, P=0.041) of the patients who not received surgical treatment were more obvious than those who received surgical treatment. When it talked about living in a city or a country, it showed that only differences in anxiety(t=2.273, P=0.032). CONCLUSION:S During the period of COVID-19, the anxiety and depression symptoms arise between breast cancer patients. This phenomenon deserves special attention by the society and medical staff.