\begin{tikzpicture}%[every node/.style={scale=0.7}]

% configurable parameters
\def\eps{0.1};
\coordinate[label = {right:$t_0-i\beta$}] (t0beta) at ($(-2.0,-1.0)$) {};
\coordinate[label ={[xshift=3*\eps cm, yshift=\eps cm]$t_0$}] (t0) at ($(-2.0,0)$) {};

\coordinate (ub) at (+4.0,0);
\node at (ub) [right] {$+\infty$};

% axes
\draw [->,help lines] (-2.5, 0)--(3.5,0) node[below]{$\re(z)$};
\draw [->,help lines] (0, -1.5)--(0, 0.5) node[left]{$\im(z)$};

% path
\draw[
    domain=-2.0:4,
    densely dotted,
    thick,
    decoration={markings, mark=at position 0.625 with {\arrow{>}}},
    postaction={decorate}
    ] plot ({\x},{\eps});

\draw[
    densely dotted,
    thick,
    ] (4.0, \eps) to[out=-30,in=+30] (4.0, -\eps);

\draw[
    domain=-2.0:4,
    densely dotted,
    thick,
    decoration={markings, mark=at position 0.375 with {\arrow{<}}},
    postaction={decorate}
    ] plot ({\x},{-\eps});

\draw[
    densely dotted,
    thick,
    decoration={markings, mark=at position 0.375 with {\arrow{<}}},
    postaction={decorate}
    ] (t0beta) -- ($(t0)-(0,\eps)$);

% dots and ticks
\node at ($(t0)+(0,\eps)$)[circle,fill,inner sep=0.8pt]{};
\node at (t0beta)[circle,fill,inner sep=0.8pt]{};

\draw ($(t0)+(0,1pt)$) -- ($(t0)-(0,1pt)$);
\draw ($(t0beta)-(t0)+(1pt,0)$) -- ($(t0beta)-(t0)-(1pt,0)$); 

\end{tikzpicture}