Please cite this article in press as: X. Meng et al., Dynamics of a novel nonlinear stochastic SIS epidemic model with double epidemic hypothesis, J. Math. Anal. Appl. (2015), http://dx.
AbstractIn this paper, we propose new mathematical models with nonlinear incidence rate and double epidemic hypothesis. Then we dedicate to develop a method to obtain the threshold of the stochastic SIS epidemic model. To this end, first, we investigate the stability of the equilibria of the deterministic system and obtain the conditions for the extinction and the permanence of two epidemic diseases. Second, we explore and obtain the threshold of a stochastic SIS system for the extinction and the permanence in mean of two epidemic diseases. The results show that a large stochastic disturbance can cause infectious diseases to go to extinction, in other words, the persistent infectious disease of a deterministic system can become extinct due to the white noise stochastic disturbance. This implies that the stochastic disturbance is conducive to epidemic diseases control. To illustrate the performance of the theoretical results, we present a series of numerical simulations of these cases with respect to different noise disturbance coefficients.
Winter is a long period of the annual cycle of many lakes in the northern hemisphere. Low irradiance, ice, and snow cover cause poor light penetration into the water column of these lakes. Therefore, in northern lakes, respiration often exceeds primary production leading to low dissolved oxygen concentrations. This study aimed to quantify under‐ice metabolic processes during winter in an arid zone lake with little snow cover.
This study was carried out in a mid‐latitude lake in Inner Mongolia, northern China. The study lake receives relatively high incoming solar radiation on the ice in mid‐winter, and radiation can penetrate down to the bottom sediment as the lake is shallow and the ice lacks snow cover.
Primary production and respiration were estimated during two winters using high‐frequency sensor measurements of dissolved oxygen. To quantify under‐ice metabolic processes, sensors were deployed to different depths. During both winters, sensors collected data every 10 min over several weeks.
The amount of solar radiation controlled photosynthesis under ice; temperature and photosynthesis together appeared to control respiration. The balance between gross primary production and ecosystem respiration was especially sensitive to changes in snow cover, and the balance between P and R decreased.
Our data suggest that photosynthesis by plankton, submerged plants, and epiphytic algae may continue over winter in shallow lakes in mid‐latitudes when there is no snow cover on the ice, as may occur in arid climates. The continuation of photosynthesis under ice buffers against dissolved oxygen depletion and prevents consequent harmful ecosystem effects.
Nutrients may be eliminated from ice when liquid water is freezing, resulting in enhanced concentrations in the unfrozen water. The nutrients diluted from the ice may contribute to accumulated concentrations in sediment during winter and an increased risk of algae blooms during the following spring and summer. The objective of this study was to evaluate the influence of ice cover on nitrogen (N) and phosphorus (P) concentrations in the water and sediment of a shallow lake, through an examination of Ulansuhai Lake, northern China, from the period of open water to ice season in 2011-2013. The N and P concentrations were between two and five times higher, and between two and eight times higher, than in unfrozen lakes, respectively. As the ice thickness grew, contents of total N and total P showed C-shaped profiles in the ice, and were lower in the middle layer and higher in the bottom and surface layers. Most of the nutrients were released from the ice to liquid water. The results confirm that ice can cause the nutrient concentrations in water and sediment during winter to increase dramatically, thereby significantly impacting on processes in the water environment of shallow lakes.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.