  A three equation differential biodiversity model depicting spread and
propagation of Hantavirus epidemic amongst rodent species under the influence
of alien competing mouse species was introduced by Peixoto and Abramson in
2006. We analyze the Caputo time-fractional version of the Biodiversity model
along with added optimal control parameters as done by Yusof, Abdullah et al. A
new algorithm is proposed to solve fractional differential equations which is
derived from the implementation of Daftardar-Jafari Method(DJM) and implicit
$\theta$-method with $\theta=1$. This newly proposed algorithm is then used to
integrate the Optimal controlled Caputo time-fractional version of Biodiversity
Hantavirus model (OC-CTFBH model). The obtained solutions are plotted and
analyzed further for the effects of parameter variations.
