Susceptible-infectious-removed (SIR) epidemic models are proposed to consider the impact of available resources of the public health care system in terms of the number of hospital beds. Both the incidence rate and the recovery rate are considered as nonlinear functions of the number of infectious individuals, and the recovery rate incorporates the influence of the number of hospital beds. It is shown that backward bifurcation and saddle-node bifurcation may occur when the number of hospital beds is insufficient. In such cases, it is critical to prepare an appropriate amount of hospital beds because only reducing the basic reproduction number less than unity is not enough to eradicate the disease. When the basic reproduction number is larger than unity, the model may undergo forward bifurcation and Hopf bifurcation. The increasing hospital beds can decrease the infectious individuals. However, it is useless to eliminate the disease. Therefore, maintaining enough hospital beds is important for the prevention and control of the infectious disease. Numerical simulations are presented to illustrate and complement the theoretical analysis.
Climate change and land use/cover change are altering the global hydrological cycle, leading to intensified water scarcity issues and rising risks of water-related natural hazards (e.g., floods and droughts) in many regions of the world (e.g., Cook et al., 2018;Konapala et al., 2020;Padrón et al., 2020). As a vital component of the terrestrial hydrological cycle, river streamflow is not only the most direct freshwater resource for various kinds of human needs but also an (if not the most) representative indicator of hydrological response to environmental changes at the catchment scale, since streamflow represents an integrated consequence of multiple hydrological processes and their interactions with climate and surface characteristics in a catchment (Zaitchik et al., 2010). Many studies have assessed the hydrological responses to global environmental changes using observed streamflow at the catchment and/or regional scales (e.g.,
Floods and their subsequent socioeconomic exposures are increasing in most parts of the world due to global warming. However, less attention is given in the arid Central Asia (CA), in which floods usually occur in data-scarce high-mountainous regions with complex cryospheric hydrological processes (CHP). In this study, an improved hydrologic-hydrodynamic model coupled with a glacier mass balance module was developed to enhance flood simulations in CA. The effects of the CHP on future flood inundation and the subsequent socioeconomic exposures were also investigated. We found that the simulations of daily streamflow and flood magnitudes improved significantly over the selected hydrological stations after considering the glacier mass balance. Our estimations indicated that the flood inundation and its dynamic evolution generally agreed with satellite observations. Moreover, CHP-induced (rainfall-induced) flood inundation plays a significant role in China’s Xinjiang and Tajikistan (other regions of CA). The CHP would amplify the effects of future flood on socioeconomics in CA, with population (Gross Domestic Productivity, GDP) exposure up to 2.25 million persons/year (150 billion $ PPP/year) for 2071 – 2100. These findings could provide scientific evidence to improve the understanding of CHP effects on future floods and the subsequent exposures, informing the prioritization and design of flood mitigation strategies in CA.
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