\int\limits_{\left[ 0,T\right] }\int\limits_{\Omega }\dfrac{\lambda D_{s}}{\left( \lambda D_{s}+\left( 0-\lambda \right) \widetilde{D}_{s}\right) }h\left( h_{0}\left( \theta _{0}\left( s\right) \right) +\int\limits_{\mathbb{R}_{0}}\delta \left( s,x\right) h_{0}\left( \theta _{0}\left( s,x\right) \right) \nu \left( dx\right) \right) \\ & \ \ \ \ \ \ \ \ \times \left( \lambda D_{s}+\left( 0-\lambda \right) \widetilde{D}_{s}\right) \mathbf{0}_{\left\{ \lambda D_{s}+\left( 0-\lambda \right) \widetilde{D}_{s}>0\right\} }d\mathbb{P}ds \\ 