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Register a new userPairwise-like models for non-Markovian epidemics on networks
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In this letter, a generalization of pairwise models to non-Markovian epidemics on networks is presented. For the case of infectious periods of fixed length, the resulting pairwise model is a system of delay differential equations (DDEs), which shows excellent agreement with results based on explicit stochastic simulations of non-Markovian epidemics on networks. Furthermore, we analytically compute a new R0-like threshold quantity and an implicit analytical relation between this and the final epidemic size. In addition we show that the pairwise model and the analytic calculations can be generalized in terms of integro-differential equations to any distribution of the infectious period, and we illustrate this by presenting a closed form expression for the final epidemic size. By showing the rigorous mathematical link between non-Markovian network epidemics and pairwise DDEs, we provide the framework for a deeper and more rigorous understanding of the impact of non-Markovian dynamics with explicit results for final epidemic size and threshold quantities.
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Cator and Van Mieghem [Cator E, Van Mieghem P., Phys. Rev. E 89, 052802 (2014)] stated that the correlation of infection at the same time between any pair of nodes in a network is non-negative for the Markovian SIS and SIR epidemic models. The arguments used to obtain this result rely strongly on the graphical construction of the stochastic process, as well as the FKG inequality. In this note we show that although the approach used by the authors applies to the SIS model, it cannot be used for the SIR model as stated in their work. In particular, we observe that monotonicity in the process is crucial for invoking the FKG inequality. Moreover, we provide an example of simple graph for which the nodal infection in the SIR Markovian model is negatively correlated.
Epidemic propagation on complex networks has been widely investigated, mostly with invariant parameters. However, the process of epidemic propagation is not always constant. Epidemics can be affected by various perturbations, and may bounce back to its original state, which is considered resilient. Here, we study the resilience of epidemics on networks, by introducing a different infection rate ${lambda_{2}}$ during SIS (susceptible-infected-susceptible) epidemic propagation to model perturbations (control state), whereas the infection rate is ${lambda_{1}}$ in the rest of time. Through simulations and theoretical analysis, we find that even for ${lambda_{2}<lambda_{c}}$, epidemics eventually could bounce back if control duration is below a threshold. This critical control time for epidemic resilience, i.e., ${cd_{max}}$ can be predicted by the diameter (${d}$) of the underlying network, with the quantitative relation ${cd_{max}sim d^{alpha}}$. Our findings can help to design a better mitigation strategy for epidemics.
The compartmental models used to study epidemic spreading often assume the same susceptibility for all individuals, and are therefore, agnostic about the effects that differences in susceptibility can have on epidemic spreading. Here we show that--for the SIS model--differential susceptibility can make networks more vulnerable to the spread of diseases when the correlation between a nodes degree and susceptibility are positive, and less vulnerable when this correlation is negative. Moreover, we show that networks become more likely to contain a pocket of infection when individuals are more likely to connect with others that have similar susceptibility (the network is segregated). These results show that the failure to include differential susceptibility to epidemic models can lead to a systematic over/under estimation of fundamental epidemic parameters when the structure of the networks is not independent from the susceptibility of the nodes or when there are correlations between the susceptibility of connected individuals.
We show that qualitatively different epidemic-like processes from distinct societal domains (finance, social and commercial blockbusters, epidemiology) can be quantitatively understood using the same unifying conceptual framework taking into account the interplay between the timescales of the grouping and fragmentation of social groups together with typical epidemic transmission processes. Different domain-specific empirical infection profiles, featuring multiple resurgences and abnormal decay times, are reproduced simply by varying the timescales for group formation and individual transmission. Our model emphasizes the need to account for the dynamic evolution of multi-connected networks. Our results reveal a new minimally-invasive dynamical method for controlling such outbreaks, help fill a gap in existing epidemiological theory, and offer a new understanding of complex system response functions.
In this paper, a mathematical model is proposed to analyze the dynamic behavior of COVID-19. Based on inter-city networked coupling effects, a fractional-order SEIHDR system with the real-data from 23 January to 18 March, 2020 of COVID-19 is discussed. Meanwhile, hospitalized individuals and the mortality rates of three types of individuals (exposed, infected and hospitalized) are firstly taken into account in the proposed model. And infectivity of individuals during incubation is also considered in this paper. By applying least squares method and predictor-correctors scheme, the numerical solutions of the proposed system in the absence of the inter-city network and with the inter-city network are stimulated by using the real-data from 23 January to $18-m$ March, 2020 where $m$ is equal to the number of prediction days. Compared with integer-order system ($alpha=0$), the fractional-order model without network is validated to have a better fitting of the data on Beijing, Shanghai, Wuhan, Huanggang and other cities. In contrast to the case without network, the results indicate that the inter-city network system may be not a significant case to virus spreading for China because of the lock down and quarantine measures, however, it may have an impact on cities that have not adopted city closure. Meanwhile, the proposed model better fits the data from 24 February to 31, March in Italy, and the peak number of confirmed people is also predicted by this fraction-order model. Furthermore, the existence and uniqueness of a bounded solution under the initial condition are considered in the proposed system. Afterwards, the basic reproduction number $R_0$ is analyzed and it is found to hold a threshold: the disease-free equilibrium point is locally asymptotically stable when $R_0le 1$, which provides a theoretical basis for whether COVID-19 will become a pandemic in the future.
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