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Environmental factors associated with climate change such as increasing sea surface temperature (SST) and solar radiation (SR) have negatively impacted corals throughout their geographic ranges. One such coral, which has been seriously impacted by these stressors, is the staghorn coral Acropora cervicornis. To reduce the effects of such stressors, this coral utilizes fluorescent proteins (FPs) and melanin (M). These constitutive immune components quench reactive oxygen species (ROS) produced during thermal stress and absorb or reflect potentially damaging light. The synthesis of these components are, nonetheless, energetically costly. Hence, production of these protective compounds may be traded-off against other vital functions such as growth. In this study we develop a mathematical model, viz., a system of ordinary differential equations that simulates the growth of A. cervicornis branches under different regimes and combinations of SST and SR. The model assumes that polyps are the functional unit of the coral and that the concentration of FPs and M are inversely proportional to SST and SR intensity. To develop the model we use empirical (birth and mortality rate of polyps and the maximum number of polyps per unit area) and theoretical parameters (concentration of FPs, M produced, and trade-offs with growth). The model simulates how changes in FPs and M due to environmental changes affect the growth capacity of A. cervicornis. The model as well as its stability analysis show that polyp growth is affected by SR and SST. Hence, the model will help in understanding how corals will respond to future changes in climate.