Subjects: Mathematics >> Computational Mathematics. submitted time 2023-02-15 Cooperative journals: 《桂林电子科技大学学报》
Abstract： The aim of this paper is to estimate the risk of Zika and dengue fever (DEN)infection that imports from Asia and
causes local outbreaks. Based on the oversea epidemic data and the floating population between 2015 and 2017, an input
model was built to estimate the number of imported cases, and the local epidemic transmission probability and basic regeneration
number were calculated via the branching process under different temperatures and herd immunity levels. The imported
cases of Zika in China mainly came from Singapore, Thailand and Vietnam, with the predicted number of cases as 7.0
(95% CI:6.5-7.5), 2.0 (95% CI:1.8-2.2) and 1.0 (95% CI:0.9-1.1). The imported DEN cases were mainly from Thailand,
Malaysia, Singapore, Vietnam, Philippines, Indonesia, India and Korea, the predicted number of cases as 700.0
(95%CI:679.8-720.2), 654.1 (95%CI:641.8-666.2), 376.3 (95% CI:368.2-384.1), 277.1 (95% CI:268.6-285.3),
241.20 (95% CI:233.6-248.8), 67.03 (95% CI:59.6-74.5), 9.1 (95% CI:6.7-11.3) and 3.0 (95% CI:1.9-4.1). The
optimum temperature for Zika and DEN transmission is around 28.9 ℃, in which the risk probability of local transmission is
24.4% and 99.9%, respectively. When the human herd immunity level is 0, 0.2 and 0.6, the basic reproduction numbers
of Zika and DEN are 8.1, 6.7, 3.2 and 3.2, 2.7, 1.3, respectively. The imported cases mainly come from South Asia.
South-central and south-eastern China are top-risk areas for local transmission, especially in June-August. The infection in
Singapore is more likely to cause Zika outbreak in China, while the infection in Thailand, Vietnam, Malaysia and Singapore
are the biggest cause of local transmission of DEN in China.
Subjects: Mathematics >> Computational Mathematics. submitted time 2023-02-15 Cooperative journals: 《桂林电子科技大学学报》
Abstract： In order to further improve the numerical accuracy of solving Volterra integro-differential, two kinds of Legendre
spectral Galerkin numerical integration methods are investigated for the Volterra-type integro-differential equation with variable
coefficients. Firstly, the Galerkin Legendre numerical integration is applied to deal with the integral term of the Volterra-
type integro-differential equations. Secondly, the Legendre tau scheme is developed for the Volterra-type integral-differential
equations with variable coefficient, and the Chebyshev-Gauss-Lobatto collocation point is used to the calculation of the
variable coefficient and integral term. Finally, by decomposing the definition interval of the function, the multi-interval Legendre
spectral Galerkin numerical integration method is also designed. Its scheme of the proposed method has symmetric
structure for odd-order model. In addition, by introducing the least squares function of the Volterra type integro-differential
equation, the Legendre spectral Galerkin least-squares numerical integration method of is constructed. The corresponding
coefficient matrix of the algebraic equation is symmetric positive. Some numerical examples are given to test the high-order
accuracy and the effectiveness of our methods.
Subjects: Mathematics >> Applied Mathematics submitted time 2022-10-19 Cooperative journals: 《桂林电子科技大学学报》
Abstract： As the extension of a complementarity problem, the weighted complementarity problem is an important kind of equilibrium problem, which could be used to model a larger class of practical equilibrium problems in economy and finance.Because of the nonzero weight vector, the weighted complementarity problem is usually more complicated than the complementarity problem. There is little available work about the algorithms for the weighted complementarity problem. In this paper, an interior-point algorithm is extended from linear optimization to weighted complementarity problems. Based on an equivalent reformulation of central path, a full-modified-Newton step feasible interior-point algorithm is proposed for solving a class of linear weighted complementarity problems over the nonnegative orthant. There is no linear search at each iteration.Under appropriate assumptions, we prove the feasibility of the algorithm, and obtain the iteration complexity. The numerical results illustrate that the algorithm is effective.
Subjects: Mathematics >> Applied Mathematics submitted time 2022-09-27 Cooperative journals: 《桂林电子科技大学学报》
Abstract： Two parameters for Brownian motion and the increment of the law of the iterated logarithm problem, using two parameter Brownian motion and increment as a tool, the law of the iterated logarithm for large deviation of Brownian motion and its incremental results about violations of the law of the iterated logarithm for the appropriate improvement, and promote the Brownian motion of two parameters, finally got two parameters Brownian motion increment of triple logarithmic law. Two parameters of Brownian motion is made up of Brownian motion is derived, with a series of and the probability of Brownian motion corresponding to the nature and the characteristics of the analysis, so with the help of predecessors, Brownian motion and Brownian motion increment of the law of the iterated logarithm for research, the two parameters of Brownian motion law of the iterated logarithm for qualification, reinforced conditions after the two parameters of the Brownian motion of a functional limit as a result, the two parameters of the Brownian motion of incremental triple logarithmic law. The theory verifies the correctness of the results.
Subjects: Mathematics >> Theoretical Computer Science submitted time 2022-09-27 Cooperative journals: 《桂林电子科技大学学报》
Abstract： To solve the reasonable allocation of campus resources, optimize the operation mode of the campus public transportation system, and meet the daily convenient travel of teachers and students, an optimization scheme of campus bus system based on 0-1 integer programming model was proposed.The study took Guilin University of Electronic Technology as an example, firstly, the present situation of student travel was investigated, the result shows that most students are willing to use campus bus, which means campus bus has certain development prospects. Through field measurement and collection of relevant geographical data, 0-1 integer planning was used to select the location of bus stops and ant colony algorithm was applied to optimize bus routes, and made a series of simulation experiments to test the carrying capacity of the campus bus system. Finally, it was concluded that the distribution location of 19 bus stations and the loop length generated by the optimal bus route is 4 805 meters, and under the restriction of the vehicle driving speed within 20km/h, at least 15 buses should be arranged to meet the time needs of most students. The results show that the optimized campus bus system planning is more reasonable, which meets the ravel needs of most teachers and students and is suitable for small and medium-sized campus traffic route planning.
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