We propose simple agent-based mathematical model of epidemic development capable to generate various multi-peak dynamics typical to COVID-19 pandemic. Agents are supplied with very simple kind behavior moving in a homogeneous interaction space with a constant speed. There is a probability of infection transmission if the agents meet with at certain distance. Next we assume that our agents get three features of intelligences called here: (i) information induced feedback, (ii) delay reaction on danger and (iii) danger adaptation. All these features are accounted in the model by the infection probability that becomes dynamic variable driven by additional differential equation. The information feedback means that this probability decreases with growing number of infected cases. It reflects facts that in modern world information media monitor the pandemic situation and with progressing infection around people start to protect them carefully that finally leads to the decrease of infected cases. Characteristic timings accounted in our model by delay reaction on the information feedback and danger adaptation time are also important in the probability dynamics. Surprisingly, but within these simple assumptions that did not touch any molecular specificity of COVID-19, except quite long exposure time, we immediately get a multi-peak dynamics of the pandemic development. Here, we show different conceptual cases of how such rhythmicity evolves under different parametric conditions.