A signature for biological heterogeneity in susceptibility to HIV infection?

Data on female sex workers and sero-discordant couples indicate a pattern of waning of the risk of HIV infection with longer duration of exposure to infected partners.Understanding risk of HIV acquisition and transmission is critical to understanding HIV epidemiology and informing prevention interventions.Informed by empirical data,we aimed to develop a statistical model to explain these observations.In our proposed model,the time to infection for each individual is exponentially distributed,but the marginal(population averaged)distribution of time to infection follows a Weibull distribution with shape parameter of about 0.5,and with the L
evy distribution being the mixing distribution.Simulations based on this model demonstrated how HIV epidemics are destined to emerge rapidly,because of the rapid sero-conversion upon exposure,but also simultaneously destined to saturate and decline rapidly after emergence,just as observed for the HIV epidemics in sub-Saharan Africa.These results imply considerable individual variability in infection risk,probably because of biological heterogeneity in the susceptibility to HIV infection.Factoring this variability in mathematical models,through the methodology provided here,could be critical for valid estimations of impact of HIV interventions and assessments of cost-effectiveness.

Effect of mixed infection on TB dynamics

Poor living conditions,overcrowding and strain diversity are some of the factors that influence mixed infection in Tuberculosis (TB) at the population level.We formulate a mathematical model for mixed infection in TB using nonlinear ordinary differential equa-tions where such factors were represented as probabilities of acquiring mixed infection.A qualitative analysis of the model shows that it exhibits multiple endemic equilibria and backward bifurcation for certain parameter values.The reactivation rate and trans-mission rate of individuals with mixed infection were of importance as well as the prob-abilities for latent individuals to acquire mixed infection.We calculate the prevalence of mixed infection from the model and the effect of mixed infection on TB incidence,TB prevalence and Mycobacterium tuberculosis (MTB) infection rate.Numerical simu-lations show that mixed infection may explain high TB incidences in areas which have a high strain diversity,poor living conditions and are overcrowded even without HIV.

Evaluating the probability of silent circulation of polio in small populations using the silent circulation statistic

As polio-endemic countries move towards elimination,infrequent first infections and incomplete surveillance make it difficult to determine when the virus has been eliminated from the population.Eichner and Dietz[American Journal of Epidemiology,143,8(1996)]proposed a model to estimate the probability of silent polio circulation depending upon when the last paralytic case was detected.Using the same kind of stochastic model they did,we additionally model waning polio immunity in the context of isolated,small,and unvaccinated populations.We compare using the Eichner and Dietz assumption of an initial case at the start of the simulation to a more accurate determination that observes the first case.The former estimates a higher probability of silent circulation in small populations,but this effect diminishes with increasing model population.We also show that stopping the simulation after a specific time estimates a lower probability of silent circulation than when all replicates are run to extinction,though this has limited impact on small populations.Our extensions to the Eichner and Dietz work improve the basis for decisions concerning the probability of silent circulation.Further model realism will be needed for accurate silent circulation risk assessment.