In this paper, we perform theoretical analyses on the behaviour of an\nevolutionary algorithm and a randomised search algorithm for the dynamic vertex\ncover problem based on its dual formulation. The dynamic vertex cover problem\nhas already been theoretically investigated to some extent and it has been\nshown that using its dual formulation to represent possible solutions can lead\nto a better approximation behaviour. We improve some of the existing results,\ni.e. we find a linear expected re-optimization time for a (1+1) EA to\nre-discover a 2-approximation when edges are dynamically deleted from the\ngraph. Furthermore, we investigate a different setting for applying the\ndynamism to the problem, in which a dynamic change happens at each step with a\nprobability $P_D$. We also expand these analyses to the weighted vertex cover\nproblem, in which weights are assigned to vertices and the goal is to find a\ncover set with minimum total weight. Similar to the classical case, the dynamic\nchanges that we consider on the weighted vertex cover problem are adding and\nremoving edges to and from the graph. We aim at finding a maximal solution for\nthe dual problem, which gives a 2-approximate solution for the vertex cover\nproblem. This is equivalent to the maximal matching problem for the classical\nvertex cover problem.\n