{k1 = 1.1, k2 = 0.1, k3 = 0.8, e = 100, s = 100, c = 1, p = 1,
  numOfReaction = 100, numOfsim = 10};

sim = NestList[(
     [CapitalDelta]t1 =
      RandomVariate@ExponentialDistribution[k1  #[[2]] #[[3]]];
     [CapitalDelta]t2 =
      RandomVariate@ExponentialDistribution[k2  #[[4]]];
     [CapitalDelta]t = Min[[CapitalDelta]t1, [CapitalDelta]t2];
     If[[CapitalDelta]t1 < [CapitalDelta]t2, {#[[
         1]] + [CapitalDelta]t, #[[2]] - 1, #[[3]] - 1, #[[4]] +
        1}, {#[[1]] + [CapitalDelta]t, #[[4]] - 1, #[[2]] +
        1, #[[3]] + 1}]) &, {0, e, s, c}, numOfReaction];

ListStepPlot[{Transpose@{sim[[All, 1]], sim[[All, 2]]},
  Transpose@{sim[[All, 1]], sim[[All, 4]]}},
 PlotLegends -> {"Simulation"},
 PlotStyle -> Directive[AbsoluteThickness[0.2]], Frame -> True,
 PlotTheme -> "Detailed", FrameLabel -> {"Time", "Population"},
 ImageSize -> Large]

NestList[(
   [CapitalDelta]t1 =
    RandomVariate[ExponentialDistribution[k1  #[[2]] #[[3]]]];
   [CapitalDelta]t2 =
    RandomVariate[ExponentialDistribution[k2  #[[4]]]];
   [CapitalDelta]t3 =
    RandomVariate[ExponentialDistribution[k3  #[[4]]]];
   [CapitalDelta]t =
    Min[{[CapitalDelta]t1, [CapitalDelta]t2, [CapitalDelta]t3}];
   If[[CapitalDelta]t1 < [CapitalDelta]t2, {#[[
       1]] + [CapitalDelta]t, #[[2]] - 1, #[[3]] - 1, #[[4]] +
      1}, {#[[4]] - 1, #[[2]] + 1, #[[3]] + 1}];
   If[[CapitalDelta]t1 < [CapitalDelta]t3, {#[[
       1]] + [CapitalDelta]t, #[[2]] - 1, #[[3]] - 1, #[[4]] +
      1}, {#[[4]] - 1, #[[2]] + 1, #[[5]] + 1}];
   If[[CapitalDelta]t2 < [CapitalDelta]t3, {#[[
       1]] + [CapitalDelta]t, #[[4]] - 1, #[[2]] + 1, #[[3]] +
      1}, {#[[4]] - 1, #[[2]] + 1, #[[4]] + 1}]) &, {0, e, s,
  c}, numOfReaction]