We consider the problem of reliable information propagation in the brain using biologically realistic models of spiking neurons. Biological neurons use action potentials, or spikes, to encode information. Information can be encoded by the rate of asynchronous spikes or by the (precise) timing of synchronous spikes. Reliable propagation of synchronous spikes is well understood in neuroscience and is relatively easy to implement by biologically-realistic models of neurons. However, reliable propagation of rate-modulated asynchronous spikes is poorly understood and remains difficult to implement by those models. In this paper, we formulate how a multi-layered feedforward neural network (mlFNN) comprising biologically-plausible model neurons enables propagation of time-varying asynchronous spikes. Gradient descent algorithm is developed to estimate the connectivity between neurons (i.e., synaptic weights) in mlFNN. Furthermore, we propose an abstract network model to replicate information propagation in mlFNN with substantially less complexity in estimating synaptic weights. The abstract model has a great implication for neuromorphic computing, as it can be implemented in neuromorphic circuits with less complexity, less energy, and more speed. Simulation results demonstrate that (i) the mlFNN with optimal synapses transmits asynchronous spikes reliably, and (ii) the abstract network model reproduces information propagation performed by mlFNN with high accuracy (coding fraction = 0.97 ± 0.02). We anticipate that this study will facilitate the design and implementation of biologically realistic mlFNN in neuromorphic circuits as well as cross-fertilizations between the fields of neuromorphic engineering, computational neuroscience and artificial intelligence.