By　collecting　various　control　policies　taken　by　127　countries/territories　during　the　first　wave　of　COVID-19　pandemic　until　July　2nd,　2020,　we　evaluate　their　impacts　on　the　epidemic　dynamics　quantitatively　through　a　combination　of　the　multiple　linear　regression,　neural-network-based　nonlinear　regression　and　sensitivity　analysis.　Remarkable　differences　in　the　public　health　policies　are　observed　across　these　countries,　which　affect　the　spreading　rate　and　infected　population　size　to　a　great　extent.　Several　key　dynamical　features,　like　the　normalized　cumulative　numbers　of　confirmed/cured/death　cases　on　the　100th　day　and　the　half　time,　show　statistically　significant　linear　correlations　with　the　control　measures,　which　thereby　confirms　their　dramatic　impacts.　Most　importantly,　we　perform　the　mediation　analysis　on　the　SEIR-QD　model,　a　representative　of　general　compartment　models,　by　using　the　structure　equation　modeling　for　multiple　mediators　operating　in　parallel.　This,　to　the　best　of　our　knowledge,　is　the　first　of　its　kind　in　the　field　of　epidemiology.　The　infection　rate　and　the　protection　rate　of　the　SEIR-QD　model　are　confirmed　to　exhibit　a　statistically　significant　mediation　effect　between　the　control　measures　and　dynamical　features　of　epidemics.　The　mediation　effect　along　the　pathway　from　control　measures　in　Category　2　to　four　dynamical　features　through　the　infection　rate,　highlights　the　crucial　role　of　nucleic　acid　testing　and　suspected　cases　tracing　in　containing　the　spread　of　the　epidemic.　Our　data-driven　analysis　offers　a　deeper　insight　into　the　inherent　correlations　between　the　effectiveness　of　public　health　policies　and　the　dynamic　features　of　COVID-19　epidemics.