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Multistrain diseases, which are infected through individual contacts, pose severe public health threat nowadays. In this paper, we build competitive and mutative two‐strain edge‐based compartmental models using probability generation function (PGF) and pair approximation (PA). Both of them are ordinary differential equations. Their basic reproduction numbers and final size formulas are explicitly derived. We show that the formula gives a unique positive final epidemic size when the reproduction number is larger than unity. We further consider competitive and mutative multistrain diseases spreading models and compute their basic reproduction numbers. We perform numerical simulations that show some dynamical properties of the competitive and mutative two‐strain models. 相似文献
65.
本文针对求矩阵方程AXB+CXD=F唯一解的参数迭代法,分析当矩阵A,B,C,D均是Hermite正(负)定矩阵时,迭代矩阵的特征值表达式,给出了最优参数的确定方法,并提出了相应的加速算法. 相似文献
66.
This paper develops a framework to deal with the unconditional superclose analysis of
nonlinear parabolic equation. Taking the finite element pair $Q_{11}/Q_{01} × Q_{10}$ as an example,
a new mixed finite element method (FEM) is established and the $τ$ -independent superclose
results of the original variable $u$ in $H^1$-norm and the flux variable $\mathop{q} \limits ^{\rightarrow}= −a(u)∇u$ in $L^2$-norm are deduced ($τ$ is the temporal partition parameter). A key to our analysis is an
error splitting technique, with which the time-discrete and the spatial-discrete systems are
constructed, respectively. For the first system, the boundedness of the temporal errors is obtained. For the second system, the spatial superclose results are presented unconditionally, while the previous literature always only obtain the convergent estimates or require
certain time step conditions. Finally, some numerical results are provided to confirm the
theoretical analysis, and show the efficiency of the proposed method. 相似文献
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The edge‐percolation and vertex‐percolation random graph models start with an arbitrary graph G, and randomly delete edges or vertices of G with some fixed probability. We study the computational complexity of problems whose inputs are obtained by applying percolation to worst‐case instances. Specifically, we show that a number of classical ‐hard problems on graphs remain essentially as hard on percolated instances as they are in the worst‐case (assuming ). We also prove hardness results for other ‐hard problems such as Constraint Satisfaction Problems and Subset‐Sum, with suitable definitions of random deletions. Along the way, we establish that for any given graph G the independence number and the chromatic number are robust to percolation in the following sense. Given a graph G, let be the graph obtained by randomly deleting edges of G with some probability . We show that if is small, then remains small with probability at least 0.99. Similarly, we show that if is large, then remains large with probability at least 0.99. We believe these results are of independent interest. 相似文献
69.
It is shown that for , there exists an optimal packing with triples on points that contains no Pasch configurations. Furthermore, for all (mod 6), there exists a pairwise balanced design of order , whose blocks are all triples apart from a single quintuple, and that has no Pasch configurations amongst its triples. 相似文献
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