Mathematical Model Of Population Dynamics And Information Security

With the progress of science and technology, especially the rapid development of com-puter technology, the vocabulary of mathematical model is also more and more appear inthe production, work and social activities of modern people. The mathematical model isa science of mathematical theory combined with the practical problems. It reduce the realproblem to corresponding mathematical problem, and on this basis, using mathematicalconcepts, methods and theoretical to analysis and research.Then use the qualitative andquantitative point to describe the practical problems, and provide accurate data and reli-able guidance for solving practical problems.For the majority of the scientifc and technicalpersonnel and applied mathematicians, mathematical model is an essential bridge betweenthe mathematical tools they have and practical problem placed in front of them.This paper mainly studies the malaria transmission model with population dynamicin patches and the secret level valuation method of BLP model based on some applicationproperties the information security by establishing a mathematical model.The main work isas follows:1.In chapter2,a malaria model with population dynamic in two patches is established,which the hosts can migrate between patches, but not the vectors. We demonstrate thatthe model is irreducible cooperative and strongly monotone. Then we compute the basicreproduction number R0.We prove that if R01, then the disease-free equilibrium is glob-ally asymptotically stable. When R0>1, we prove that there exists a unique endemicequilibrium, which is globally asymptotically stable.2.In chapter3,according to the access attribute properties between subjects and objectsin the information system, a viable method of the BLP model secret level valuation is given,and two merging conditions are putted forward. The mathematical model of subject-objectsecret level valuation under BLP model is established on the two merging conditions. Whenthe condition solution is not the constant one, its expansion solution being not sure theglobal one is proved, but the approximate condition modifcation valuation solution can be obtained from it. Using above results, one difcult problem from one national informationsystem about the BLP model secret level valuation is solved.