The aim of this paper is to statistically examine whether there are different patterns in daily numbers of deaths during the quiet periods of solar activity, in contrast to the periods of the strong solar storms. We considered three periods of solar storms (storm of 14 July 2000 Bastille Day Event, storm of 28 October 2003 Halloween Solar Storms, and storm of 17 March 2015 St. Patrick’s Day event) and three periods of continuous very low solar activity (13 September–24 October 1996, 21 July–20 August 2008, and 31 July–31 August 2009) during the Solar Cycles No. 23 and No. 24. In particular, we focus on diseases of the nervous system (group VI from ICD-10) and diseases of the circulatory system (group IX from ICD-10) separately for both sexes and two age groups (under 39 and 40+). We demonstrate that in the resulting graphical models there was a connection between the daily number of deaths and all indices of solar and geomagnetic activity in periods of low solar activity in contrast to periods of strong solar storms in some monitored groups according to age, sex, and group of diagnosis.