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The study of epidemics spreading with community structure has become a hot topic. The classic S I R epidemic model does not distinguish between dead and recovered individuals. It is inappropriate to classify dead individuals as recovered individuals because the real-world epidemic spread processes show different recovery rates and death rates in different communities. In the present work, a S I R D epidemic model with different recovery rates is proposed. We pay more attention to the changes in the number of dead individuals. The basic reproductive number is obtained. The stationary solutions of a disease-free state and an endemic state are given. We show that quarantining communities can decrease the basic reproductive number, and the total number of dead individuals decreases in a disease-free steady state with an increase in the number of quarantined communities. The most effective quarantining strategy is to preferentially quarantine some communities/cities with a greater population size and a fraction of initially infected individuals. Furthermore, we show that the population flows from a low recovery rate and high population density community/city/country to some high recovery rate and low population density communities/cities/countries, which helps to reduce the total number of dead individuals and prevent the prevalence of epidemics. The numerical simulations on the real-world network and the synthetic network further support our conclusions. [ABSTRACT FROM AUTHOR]

Multilayer networks are widely used to characterize the dynamic behavior of complex systems. The study of epidemic spreading dynamics on multilayer networks has become a hot topic in network science. Although many models have been proposed to explore epidemic spreading across different networks, there is still a lack of models to study the spreading of diseases in the process of evolution on multilayer homogeneous networks. In the present work, we propose an epidemic spreading dynamic model of homogeneous evolving networks that can be used to analyze and simulate the spreading of epidemics on such networks. We determine the global epidemic threshold. We make the interesting discovery that increasing the epidemic threshold of a single network layer is conducive to mitigating the spreading of an epidemic. We find that the initial average degree of a network and the evolutionary parameters determine the changes in the epidemic threshold and the spreading process. An approach for calculating the falling and rising threshold zones is presented. Our work provides a good strategy to control epidemic spreading. Generally, controlling or changing the threshold in a single network layer is easier than trying to directly change the threshold in all network layers. Numerical simulations of small-world and random networks further support and enrich our conclusions. [ABSTRACT FROM AUTHOR]