Migration can be divided into temporary and permanent migration, which is related to the residence time of people in the patch, thus we consider an SIS epidemic model with migration and residence time in a patchy environment. If [Formula: see text], the disease-free equilibrium is globally asymptotically stable and the disease dies out. With the same migration rate of susceptible and infectious individuals and without disease-induced death, when [Formula: see text], the endemic equilibrium is unique and globally asymptotically stable. Numerical simulations are carried out to show the effects of residence time and the migration rate on disease prevalence.
A fractional order susceptible–exposed–infected–quarantined–recovered model is established on the complex networks. We calculate a specific expression for the basic reproduction number [Formula: see text], prove the existence and uniqueness with respect to the solution, and prove the Ulam–Hyers stability of the model. Using the Latin hypercube sampling-partial rank correlation coefficient method, the influence of parameters on the [Formula: see text] is analyzed. Based on the results of the analysis, the optimal control of the model is investigated as the control variables with vaccination rate and quarantine rate applying Pontryagin’s minimum principle. The effects of [Formula: see text], degree of nodes, and network size on the model dynamics are simulated separately by the prediction correction method.
Objective:Current methods for the diagnosis of ventriculoperitoneal (VP) shunt malfunction lack specific standards; therefore, it may be missed or misdiagnosed. Hence, providing a reliable diagnostic method will help improve the accuracy of preoperative decision-making. Therefore, the aim of the study was to provide a new method for the diagnosis of VP shunt malfunction.Methods:After in vitro testing, we enrolled a total of 12 patients with VP shunt malfunction. Before revision surgery, 0.1 mL of a 5% sodium valproate (SV) solution was injected into the reservoir; 0.1 mL of the cerebrospinal fluid (CSF) was withdrawn 20 minutes later from the reservoir to measure the SV concentration. The process was repeated on the seventh day after surgery and compared with the preoperative results.Results:The mean ± standard deviation preoperative SV concentration in the cerebrospinal fluid was greater than the postoperative concentration (5967.8 ± 1281.3 vs 391.1 ± 184.6 μg/mL, P = .001).Conclusion:The proposed method is a reliable, safe, and relatively simple alternative for the diagnosis of VP shunt malfunction and further provides a reference for treatment.
In this paper, we propose a susceptible-infected-susceptible (SIS) epidemic model with demographics on heterogeneous metapopulation networks. We analytically derive the basic reproduction number, which determines not only the existence of endemic equilibrium but also the global dynamics of the model. The model always has the disease-free equilibrium, which is globally asymptotically stable when the basic reproduction number is less than unity and otherwise unstable. We also provide sufficient conditions on the global stability of the unique endemic equilibrium. Numerical simulations are performed to illustrate the theoretical results and the effects of the connectivity and diffusion. Furthermore, we find that diffusion rates play an active role in controlling the spread of infectious diseases.
In this article, an SEAIRS model of COVID-19 epidemic on networks is established and analyzed. Following the method of the next-generation matrix, we derive the basic reproduction number R0, and it shows that the asymptomatic infector plays an important role in disease spreading. We analytically show that the disease-free equilibrium E0 is asymptotically stable if R0≤1; moreover, the effects of various quarantine strategies are investigated and compared by numerical simulations. The results obtained are informative for us to further understand the asymptomatic infector in COVID-19 propagation and get some effective strategies to control the disease.
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