The　minimal　case　fatality　rate　(CFR)　is　one　of　the　essential　fundaments　for　the　establishment　of　a　diverse　national　response　strategy　against　the　COVID-19　epidemic,　but　cannot　be　quantitatively　predicted.　The　aim　of　the　present　study　was　to　explore　the　applicable　quantitative　parameters　labeling　integrating　responding　capacity　from　national　daily　CFR　curves,　and　whether　the　minimal　CFR　during　initial　emerging　epidemic　outbreaks　can　be　predicted.　We　analyzed　data　from　214　nations　and　regions　during　the　initial　2020　COVID-19　epidemic　and　found　similar　falling　zones　marked　with　two　turning　points　within　a　fitting　three-day-moving　CFR　curve　which　occurred　for　many　nations　and　regions.　The　turning　points　can　be　quantified　with　parameters　for　the　day　duration　(T1,　T2,　and　Delta　T)　and　for　the　three-day　moving　arithmetic　average　CFRs　(CFR1,　CFR2,　and　Delta　CFR)　under　wave　theory　for　71　nations　and　regions　after　screening.　Two　prediction　models　of　minimal　CFR　were　established　with　multiple　linear　regressions　(M1)　and　multi-order　curve　regressions　(M2)　after　internal　and　external　evaluation.　Three　kinds　of　falling　zones　could　be　classified　in　the　other　71　nations　and　regions.　Only　the　minimal　CFR　showed　significant　correlations　with　nine　independent　national　indicators　in　65　nations　and　regions　with　CFRs　less　than　7%.　Model　M1　showed　that　logarithmic　population,　births　per　1000　people,　and　household　size　made　significant　positive　contributions,　and　logarithmic　GDP,　percentage　of　population　aged　65+　years,　domestic　general　government　health　expenditure,　physicians　per　1000　people,　nurses　per　1000　people,　and　body　mass　index　made　negative　contributions　to　the　minimal　CFR　against　COVID-19　epidemics　for　most　nations　and　regions.　The　spontaneous　minimal　CFR　was　predicted　well　with　model　M1　for　57　nations　and　regions　based　on　the　nine　national　indicators　(R-2　=　0.5074),　or　with　model　M2　for　59　nations　and　regions　based　on　the　nine　national　indicators　(R-2　=　0.8008)　at　internal　evaluation.　The　study　confirmed　that　national　spontaneous　minimal　CFR　could　be　predicted　with　models　successfully　for　most　nations　and　regions　against　COVID-19　epidemics,　which　provides　a　critical　method　to　predict　the　essential　early　evidence　to　evaluate　the　integrating　responding　capacity　and　establish　national　responding　strategies　reasonably　for　other　emerging　infectious　diseases　in　the　future.