Problem B The Next Plague? 2014.11.4

Simple analysis 150 Nearby villages and islands 15

Simple analysis We want to get the following results Allocate the scarce resources Classification of types & severity If an epidemic is contained or not Appropriate measures Epidemic analysis problem Disease control problems

Simple analysis Kink 4 Stage Theory 1st stage:The asymptomatic period． Unnoticed、lower morbidity 2nd stage:outbreak and spreading phase． Begin to take measures、higher morbidity 3rd stage:Peak period． Strict measures、controlled、stable 4th stage:recession and effectively control period． Patient numbers fell Develop a model to show the four stages use the model to predict the epidemic changes 建立的模型就应该体现4个不同时期下疫情的发展过程，并能够在此基础上准确预测疫情变化情况，提出切实可行的控制措施.考虑在经典传染病SIR模型基础上，通过机理分析，加入合理的实际因素，建立适合分段微分方程模型，称为SIR改进模型

Proper useful model Classification problem Analytic Hierarchy Process Cluster analysis Decision-making tree

Proper useful model Assignment problem Infectious Disease Diffusion Model Integer Programming Theory Cluster Theory Genetic Algorithms

Tips Reasonable distribution principles Clustering the victims Non-dimensional treatment

Classical SIR model I(t) --Infectives S(t)--Susceptibles R(t)—Removed N=S+I+R

Classical SIR model Solution: Increase，then decrease to 0 Diseases spread Keep decreasing to 0 Not spread

More complex cases

Some other model Branching process Reed Logistic model Infectious disease network model and the compartment model Complex network model（neighborhood） More complex models Treatment model  Quarantine and isolation model（SEIR） Infectious kinetics model (SEIDR) IF we take measures，when it comes to different stages， we can develop a model group！

For example Take borderline cases into consideration No control SE：ΔE=I(t)*r*Δt r：Contacting number EQ：ΔQ=ΔE*λ λ ：rate of virus carrier QI：ΔI=(1-(1-1/(a2-a1))exp(-t)*ΔQ*Δt Assumption: Exponential growth IR：ΔR=(1-1/a3))exp(-t)*I(t)*Δt a3:removed rate

For example Similarly， Under control function：。。。。 after before

Solving numerical analysis Fitting Iterative 。。。

Thank you！