Epidemics, apart from affecting the health of populations, can have large impacts on their social and economic behavior and subsequently feed back to and influence the spreading of the disease. This calls for systematic investigation which factors affect significantly and either beneficially or adversely the disease spreading and regional socio-economics. Based on our recently developed hybrid agent-based socio-economy and epidemic spreading model we perform extensive exploration of its six-dimensional parameter space of the socio-economic part of the model, namely, the attitudes towards the spread of the pandemic, health and the economic situation for both, the population and government agents who impose regulations. We search for significant patterns from the resulting simulated data using basic classification tools, such as self-organizing maps and principal component analysis, and we monitor different quantities of the model output, such as infection rates, the propagation speed of the epidemic, economic activity, government regulations, and the compliance of population on government restrictions. Out of these, the ones describing the epidemic spreading were resulting in the most distinctive clustering of the data, and they were selected as the basis of the remaining analysis. We relate the found clusters to three distinct types of disease spreading: wave-like, chaotic, and transitional spreading patterns. The most important value parameter contributing to phase changes and the speed of the epidemic was found to be the compliance of the population agents towards the government regulations. We conclude that in compliant populations, the infection rates are significantly lower and the infection spreading is slower, while the population agents’ health and economical attitudes show a weaker effect.