The use of mathematical models in the epidemiological study of infectious diseases and in the design of mass immunization programmes

The relationship between the number of people vaccinated for an infectious disease and the resulting decrease in incidence of the disease is not straightforward and linear because many independent variables determine the course of infection. However, these variables are quantifiable and can therefore by used to model the course of an infectious disease and impact of mass vaccination. Before one can construct a model, one must know for any specific infectious disease the number of individuals in the community protected by maternally derived antibodies, the number susceptible to infectious the number infected but not yet infectious (i.e., with latent infection), the number of infectious individuals, and the number of recovered (i.e., immune) individuals. Compartmental models are sets of differential equations which describe the rates of flow of individuals between these categories. Several major epidemiologic concepts comprise the ingredients of the model: the net rate of infection (i.e., incidence), the per capita rate of infection, the Force of Infection, and the basic reproductive rate of infection. When a community attains a high level of vaccination coverage, it is no longer necessary to vaccinate everyone because the herd immunity of the population protects the unvaccinated because it lowers the likelihood of their coming into contact with an infectious individual. Many infections that confer lasting immunity tend to have interepidemic periods when the number of susceptibles is too low to sustain an epidemic. Mass vacination programs reduce the net rate of transmission of the infective organism; they also increase the length of the interepidemic period. Many diseases primawrily associated with children have much more serious consequences in older people and the question arises as to at what point childhood immunization will successfully prevent the more dangerous incidence of the disease in older cohorts. Mathematical models of disease transmission enable one to predict the course of epidemics, design mass vaccination programs, and be guided as to what are the relevant data that should be collected.     

Gadolinium-enhanced MR findings in a pediatric case of Wernicke encephalopathy.

This report describes the postcontrast MR findings of Wernicke encephalopathy seen in a malnourished 11-year-old boy. The examination showed increased signal on T2-weighted images in the periaqueductal gray matter and medial thalami. On T1-weighted acquisition, these areas showed decreased signal intensity, but on postcontrast T1-weighted examination, they showed moderately intense enhancement. Also noted on the postcontrast examination was mamillary body enhancement.     

Androgen receptor YAC transgenic mice carrying CAG 45 alleles show trinucleotide repeat instability

X-linked spinal and bulbar muscular atrophy (SBMA) is caused by a CAG repeat expansion in the first exon of the androgen receptor (AR) gene. Disease-associated alleles (37-66 CAGs) change in length when transmitted from parents to offspring, with a significantly greater tendency to shift size when inherited paternally. As transgenic mice carrying human AR cDNAs with 45 and 66 CAG repeats do not display repeat instability, we attempted to model trinucleotide repeat instability by generating transgenic mice with yeast artificial chromosomes (YACs) carrying AR CAG repeat expansions in their genomic context. Studies of independent lines of AR YAC transgenic mice with CAG 45 alleles reveal intergenerational instability at an overall rate of approximately 10%. We also find that the 45 CAG repeat tracts are significantly more unstable with maternal transmission and as the transmitting mother ages. Of all the CAG/CTG repeat transgenic mice produced to date the AR YAC CAG 45 mice are unstable with the smallest trinucleotide repeat mutations, suggesting that the length threshold for repeat instability in the mouse may be lowered by including the appropriate flanking human DNA sequences. By sequence-tagged site content analysis and long range mapping we determined that one unstable transgenic line has integrated an approximately 70 kb segment of the AR locus due to fragmentation of the AR YAC. Identification of the cis - acting elements that permit CAG tract instability and the trans -acting factors that modulate repeat instability in the AR YAC CAG 45 mice may provide insights into the molecular basis of trinucleotide repeat instability in humans.