实验报告
1 实验题目儿童麻疹流行蔓延的数学模型2 实验问题陈述试组建一个能描述儿童麻疹流行蔓延的数学模型,我们将考虑在接种疫苗成为有效的防疫手段之前的麻疹的流行1647年---1660年间每年麻疹病的死亡人数表一:伦敦每年麻疹死亡人数(1647---1660)年代47 48 49 50 51 52 53 54 55 56 57 58 59 60 人数5 92 3 33 33 62 8 52 11 153 15 80 6 74
可以看出,它是以2年为周期的周期性流行0.5周,在这段时期内一个被感染的孩子表面看来是正常的,但却会传染给别人,患病的孩子一直被隔离到痊愈为止,就修改你的模型,以拟合0.5周的潜伏期及2年周期性流行的观测结果3 实验目的通过表中数据,建立麻疹流行蔓延模型,以拟合0.5周的潜伏期及2年周期性流行的观测结果,判断估计出的参数是否实际4 实验内容模型假设:(1)除感病特征外,人群中的个体间没有差异,感病者与易感者的个体在人群中混合是均匀的(2)人群的数量足够大,只考虑传染过程的平均效应(3)易感者感病的机会与他接触感病者的机会成正比(4)疾病的传染率为常数(5)一般的麻疹爆发在几十天,我们不考虑在一次麻疹爆发时间内某地区的出生人口和死亡人口,以及人口的迁入和迁出(6)感病痊愈者(即移出者)移出模型,而不再成为易感者人群中的成员变量说明:S(t):易感者在人群中所占的比例I(t):感病者在人群中所占的比例R(t):移出者在人群中所占的比例 K:疾病的传染率 h:单位时间内痊愈的百分数一个传染期内每个病人有效接触易感者的平均人数,成为接触数---初始时刻问题分析:对麻疹流行蔓延的周期性质进行说明通过对SIR模型及麻疹流行的机理分析,在一次麻疹爆发以后绝大多数人体内具有了麻疹免疫抗体,因此绝大多数新生婴儿体内具有抗体,考虑到引起流行周期的原因是易感人群的积累,易感人群来源于新生儿因母体抗体逐渐消失而易感通常认为在自然感染状态下,这些易感者积累到一个以上出生队列时,就达到爆发的“临界”,出生队列出现的周期性在一定程度上可以说明麻疹流行的周期性模型建立通过对问题的分析,模型可以表示为:,其中 考虑到初始条件,可知上述三个方程是相容的,因此可以化简为:
由于方程组无法求出解析解,故可以在S-I的像平面上讨论解的性质,相轨线的定义域为:
由以上方程可知轨线的方程为:,
其解为:?
5 实验结果分析与讨论由题目中表格给出的麻疹死亡人数与年份的对应关系,用MATLAB编程画出的曲线图如图一所示:
【图一】 由于对S(t)和I(t)的求1解非常困难,所以先用数值计算的方法来预估计S(t)和I(t)的一般变化规律在方程(1)中设k=1,h=0.3,I(0)=0.02,S(0)=0.98编写MATLAB程序并运行得到如图二, 【图二】【注】图中蓝色曲线为I(t),即病人比例;绿色曲线为S(t),即健康人比例从时间流程图中可以看出,随着时间的增加,S(t)单调递减,I(t)在时达到峰值以后会随时间减小,当时,S(t)值很小,而I(t)=0,被移出除传染系统c. 对结果的分析参数中取h为0.3,则潜伏期为1/h=3.33天,约等于0.5周看到把h取为0.3得到的曲线符合实际情况,说明潜伏期为麻疹病毒的潜伏期是0.5周是正确的观点另外,当时,,,说明在一次麻疹疫情爆发以后绝大多数的人体内已经具有麻疹免疫抗体,被移出除传染系统查资料知,绝大多数的婴儿在9个月时血内的母亲抗体已测不出,有些婴儿体内的抗体存在时间可以长达15个月,所以可以取1年为一个出生队列产生的时间,用时间坐标来表示出生队列与麻疹流行周期的关系如图三:
【图三】【注】: 表示第一年的年初;表示第一年年末;表示第二年年初;表示第二年年末;在时刻出生的婴儿到时刻抗体消失,时刻出生的婴儿到时刻抗体消失易感人群从时刻开始积累,在时刻易感人群刚好积累一个出生队列,因此易感人群积累一个出生队列的时间为2年当易感人群积累到一个出生队列时,就是第二次麻疹爆发的“临界”,因此可以说麻疹流行的周期为2年综上所述,儿童麻疹流行蔓延的模型具有周期性,且以0.5周的潜伏期和2年的周期性流行故模型所得结果与题目要求是一致的6 实验程序(Matlab或者其它软件语言陈述)用MATLAB编写程序如下:(1) 画图一:x=47:60;
y=[5 92 3 33 33 62 8 52 11 153 15 80 6 74];
plot(x,y,'rp-.')
xlabel('年份'); ylabel('伦敦每年麻疹病死亡人数');(2) S(t)和I(t)的变化规律及画图三M文件为:(chuanran.m)function y=chuanran(t,x)
a=1;b=0.3;
y=[a*x(1)*x(2)-b*x(1);-a*x(1)*x(2)];
命令框中输入:>> ts=0:50;
>> x0=[0.020,0.98];
>> [t,x]=ode45('chuanran',ts,x0);
>> plot(t,x(:,1),'r*-');
>> hold on
>> plot(t,x(:,2),'b.-');
>> legend('病人的比例','健康人的比例');Acknowledgments
The authors would like to thank Johns Hopkins University for the TC-1 cells. This work was supported
by a National Health Research Institutes intramural grant (IV-103-PP-22) and grants from the National
Science Council, which were awarded to Y.C. Song (NSC 99-2321-B-400-004-MY3) and S.J. Liu (NSC
103-2321-B-400-008).
Author Contributions
Y.C.S. and S.J.L. designed the studies. Y.C.S. performed the research and analyzed the data. Y.C.S. and
S.J.L. wrote the manuscript.
Additional Information
C57BL/6 mice were immunized subcutaneously (s.c.)
once with 1 μ g of peptide mixed with or without 10 μ g of CpG adjuvant. After one week, splenocytes were
harvested, and the response of IFN-γ -secreting cells was determined by ELISPOT after 48 h of peptide
stimulation. Briefly, 2 × 105 splenocytes were incubated with 1 μ g/ml irrelevant peptide or RAH peptide
in an anti-IFN-γ -coated polyvinylidene fluoride (PVDF) plate for 48 h. After incubation, the cells were
removed, and a biotinylated anti-IFN-γ Ab (eBioscience, San Diego, CA, USA) was added to each well.
The plates were incubated at 37 °C for 2 h. Following the addition of the avidin-HRP reagent (eBioscience,
CA, USA), the assay was developed using a 3-amine-9-ethyl carbazole (AEC; Sigma-Aldrich, MO,
USA) staining solution. The reaction was stopped after 4–6 min by placing the plate under tap water.
The spots were counted using an ELISPOT reader (Cellular Technology Ltd., Shaker Heights, OH, USA).
For RAH-specific T cell staining, spleens were harvested seven days after the immunizations, and
RAH-specific CD8+ T cells were detected by tetramer staining using a PE-labeled RAH tetramer
(Beckman Coulter, CA, USA) and a FITC-labeled anti-CD8 monoclonal antibody (mAb) (eBioscience,
CA, USA). The stained RAH-specific CD8+ T cells were analyzed by flow cytometry.
Supplementary information accompanies this paper at /srep
Competing financial interests: The authors declare no competing financial interests.
How to cite this article: Song, Y.-C. and Liu, S.-J. A TLR9 agonist enhances the anti-tumor immunity
of peptide and lipopeptide vaccines via different mechanisms. Sci. Rep. 5, 12578; doi: 10.1038/
srep12578 (2015).
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reproduce the material. To view a copy of this license, visit expression of anti-apoptotic molecules such as the BCL-2 family
members BCL-XL and CASP8 and FADD-like apoptosis regulator(CFLAR, best known as cFLIP), thereby allowing CTLs to surviveand reach neoplastic
of various TLR agonists promotes the immunogenicity of DC/malignant cell fusions through the upregulation of IL-12.14,18In this setting, we used a de
from Coriolus versicolor (PSK, which operates as a TLR2 agonist)and lyophilized preparations of a low-virulence strain (Su) of
Streptococcus pyogenes (OK-432, which acts as a TLR4 agonist),both of which can be produced as good manufacturing practice
(GMP)-grade agents and have been previously used in the clinic asbiological response modifiers.18,19 Of note, DC/cancer cell fusions
activated in the presence of both TLR2 and TLR4 agonists,but not DC/malignant cell fusions that were left unstimulated
or were exposed to either TLR agonist alone, overcame theimmunosuppressive activity of tumor-derived molecules such
as transforming growth factor β1 (TGFβ1). In particular,TLR2/4-activated DCs (or the corresponding fusions): (1) exhibit
increased expression levels of MHC class II molecules and CD86on the cell surface; (2) manifest an improved fusion efficacy;
(3) produce elevated levels of IL-12; (4) simultaneously activateCD4+ and CD8+ T cells, which secrete high levels of interferon
γ (IFNγ); (5) potently induce antigen-specific CTL activity;and (6) manifest a superior efficacy in inhibiting the generation
of CD4+CD25+FOXP3+ Tregs.20 Nonetheless, when DC/cancercell fusions are generated with neoplastic cells producing extremely
high levels of TGFβ1, they inhibit the activity of CTLs in vitro.Therefore, incorporating the simultaneous activation of multiple
TLRs and the blockade of immunosuppressive that are intrinsicallyproduced by DC/neoplastic cell fusions may significantly enhancethe therapeutic potential of
this approach.Improving the Immunogenicity of Malignant CellsMost, if not all, malignant cells secrete multipleimmunosuppressive mediators such as TGFβ
molecules normally inhibit the initiation of efficient CTLresponses,21 the microenvironment of malignant cells used forthe generation of DC/cancer cell fusions
immunostimulatory. Several strategies to inhibit the production ofimmunosuppressive factors by cancer cells have been developed,
including the administration of neutralizing antibodies22 and small
chemical inhibitors,23 as well as the transfection of specific smallinterfering
RNAs (siRNAs)24 or constructs coding for a solublevariant of the TGFβ receptor.25 Also heat-shock proteins (HSPs),
which have recently been implicated in the immunogenicity ofapoptotic and necrotic cells, might constitute effective adjuvant
for boosting the efficacy of DC/neoplastic cell fusions.26,27 HSPs
generally operate as chaperons for a wide panel of peptides,
including antigenic peptides, and HSP/peptide complexes notonly can be efficiently taken up by DCs through specific receptors,but also can be presented in
molecules the DC surface.28 We have previously reported thatTLR2-stimulated DCs fused with heat-treated cancer cells are
immunogenic, as demonstrated by: (1) the upregulation of multipleHSPs, MHC class I and II molecules, TAAs, CD80, CD86, CD83,and IL-12; (2) their ability
producing high levels of IFNγ; and (3) the capacity to efficientlyelicited antigen-specific CTL activity.26 More recently, we have
demonstrated that the secretion of TGFβ1, IL-10 and VEGRfrom whole cancer cells is significantly limited upon exposure to
pharmaceutical grade ethanol, a maneuver that does not reduce theevels of MHC class I molecules and TAAs on the cell surface.27
Moreover, ethanol, employed at concentrations that affect tumorgrowth, promoted the upregulation of HSPs. HSPs exposed by
cancer cells can be recognized by DCs via TLR4, facilitating theiractivation and promoting antigen processing and presentation.29
Of note, malignant cells that undergo immunogenic apoptosisectopically expose the Ca2+-binding chaperone calreticulin (CRT)
on the cell surface, allowing TAAs to efficiently traffic to the
DC antigen-presenting compartment.30 Moreover, high-mobility
group box 1 (HMGB1) passively released from dying neoplastic
cells can stimulate antigen processing and presentation in DCs via
a TLR4-dependent signaling pathway.31,32 Therefore, the exposure
of CRT and the release of HMGB1 by ethanol-treated malignant
cells enhance the immunogenicity of DC/cancer cell fusions.27
Importantly, fusions involving DCs and ethanol-treated cancer
cells activate T cells to produce high levels of IFNγ, boosting the
elicitation of antigen-specific CTL response in vitro.27 In addition,
HSP70-peptide complexes derived from DC/cancer cell fusions
appear to possess superior immunogenic properties as compared
with similar complexes obtain from neoplastic cells.33
Synergistic Effects of Fusions Generated
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