Estimating the basic reproductive ratio for the Ebola outbreak in Liberia and Sierra Leone.

BACKGROUND: Ebola virus disease has reemerged as a major public health crisis in Africa, with isolated cases also observed globally, during the current outbreak. METHODS: To estimate the basic reproductive ratio R0, which is a measure of the severity of the outbreak, we developed a SEIR (susceptible-exposed-infected-recovered) type deterministic model, and used data from the Centers for Disease Control and Prevention (CDC), for the Ebola outbreak in Liberia and Sierra Leone. Two different data sets are available: one with raw reported data and one with corrected data (as the CDC suspects under-reporting). RESULTS: Using a deterministic ordinary differential equation transmission model for Ebola epidemic, the basic reproductive ratio R0 for Liberia resulted to be 1.757 and 1.9 for corrected and uncorrected case data, respectively. For Sierra Leone, R0 resulted to be 1.492 and 1.362 for corrected and uncorrected case data, respectively. In each of the two cases we considered, the estimate for the basic reproductive ratio was initially greater than unity leading to an epidemic outbreak. CONCLUSION: We obtained robust estimates for the value of R0 associated with the 2014 Ebola outbreak, and showed that there is close agreement between our estimates of R0. Analysis of our model also showed that effective isolation is required, with the contact rate in isolation less than one quarter of that for the infected non-isolated population, and that the fraction of high-risk individuals must be brought to less than 10% of the overall susceptible population, in order to bring the value of R0 to less than 1, and hence control the outbreak.

A comparison of a deterministic and stochastic model for hepatitis C with an isolation stage.

We formulate a deterministic epidemic model for the spread of Hepatitis C containing an acute, chronic and isolation class and analyse the effects of the isolation class on the transmission dynamics of the disease. We calculate the basic reproduction number R(0) and show that for R(0)≤1, the disease-free equilibrium is globally asymptotically stable. In addition, it is shown that for a special case when R(0)>1, the endemic equilibrium is locally asymptotically stable. Furthermore, an analogous stochastic epidemic model for Hepatitis C is formulated using a continuous time Markov chain. Numerical simulations are used to estimate the mean, variance and probability distributions of the discrete random variables and these are compared to the steady-state solutions of the deterministic model. Finally, the expected time to disease extinction is estimated for the stochastic model and the impact of isolation on the time to extinction is explored.

Network bursting using experimentally constrained single compartment CA3 hippocampal neuron models with adaptation.

The hippocampus is a brain structure critical for memory functioning. Its network dynamics include several patterns such as sharp waves that are generated in the CA3 region. To understand how population outputs are generated, models need to consider aspects of network size, cellular and synaptic characteristics and context, which are necessarily 'balanced' in appropriate ways to produce particular outputs. Thick slice hippocampal preparations spontaneously produce sharp waves that are initiated in CA3 regions and depend on the right balance of glutamatergic activities. As a step toward developing network models that can explain important balances in the generation of hippocampal output, we develop models of CA3 pyramidal cells. Our models are single compartment in nature, use an Izhikevich-type structure and involve parameter values that are specifically designed to encompass CA3 intrinsic properties. Importantly, they incorporate spike frequency adaptation characteristics that are directly comparable to those measured experimentally. Excitatory networks using these model cells are able to produce bursting suggesting that the amount of spike frequency adaptation expressed in the biological cells is an essential contributor to network bursting, and as such, may be important for sharp wave generation. The network bursting mechanism is numerically dissected showing the critical balance between adaptation and excitatory drive. The compact nature of our models allows large network simulations to be efficiently computed. This, together with the linkage of our models to cellular characteristics, will allow us to develop an understanding of population output of CA3 hippocampus with direct biological comparisons.