Nonlinear Dynamics, Bifurcation, and Chaos in a Harvested Tuna–Sardine Food Chain Model with Viral Hemorrhagic Septicemia

Tuna are among the world’s most heavily harvested marine fish, supporting global fisheries and contributing substantially to food security and coastal economies. However, the sustainability of tuna populations is increasingly threatened by the combined effects of overexploitation, ecological interactions, and infectious diseases circulating within lower trophic levels. Motivated by the occurrence of Viral Hemorrhagic Septicemia (VHS), a highly contagious viral disease affecting sardines populations, we develop a tri-trophic eco-epidemiological fishery model describing interactions among zooplankton, susceptible and VHS-infected sardines, and harvested tuna. The model incorporates predator-induced fear, refuge effects for susceptible and infected sardines, saturated disease transmission, nonlinear functional responses, and nonlinear tuna harvesting. Positivity and boundedness are established, and biologically feasible equilibria and the basic reproduction number are derived. Local and global stability, together with bifurcation behavior, are analyzed. Numerical simulations reveal stability switching, periodic oscillations, period-doubling, and chaotic dynamics, while sensitivity analysis identifies key parameters governing disease invasion. Overall, this study advances the theoretical understanding of marine eco-epidemiological dynamics and offers a quantitative basis for balancing disease control, biodiversity conservation, and sustainable exploitation of marine fishery resources.