This work presents the entropy analysis of Maxwell nanofluid containing gyrotactic microorganism in the presence of homogeneous–heterogeneous reactions with modified heat and mass flux models. Modified models are presented by utilizing Cattaneo–Christov heat flux and generalized Fick’s law. Derived equations which shows the considered flow situation are modeled in the form of PDEs under boundary layer theory, then suitable transformation is applied to convert arising PDEs into a set of transformed ODEs which are then solved using a powerful scheme namely optimal homotopy analysis procedure. Special cases of some published work are found to be in excellent agreement of our work. The impact of physical parameters on velocity, temperature, concentration, reaction rate, concentration of motile microorganism, and entropy generation are discussed graphically. Finally, the convergence of applied scheme is presented in tabular form which confirms the efficiency of applied method. It is reported that entropy generation increases for higher values of radiation parameter and Brinkman number, whereas Bejan number is reduced for the higher values of radiation and magnetic parameters. Also, fluid temperature and concentration fields are reduced by augmenting the values of Prandtl and Schmidt numbers.