In this paper, we introduce a model to study the effects of human populations on fish survival in aquatic media. Directly, this occurs by fishing. Indirectly instead this is related to other human actions that lead to organic pollution and consequently low dissolved oxygen(DO) levels, thereby harming the aquatic fauna. Mathematically, we consider various nonlinear processes involving human population, organic pollutants, bacteria, DO and fish population. In the present study, our aim is to investigate the effect of depleted level of DO on the survival of fish populations in such an aquatic system. The case study in consideration is represented by the Ulsoor lake, Bengaluru, India. Into it, huge amounts of sewage were discharged and resulted in reduction of DO level and massive fish mortality. Equilibria are analyzed for feasibility and stability, substantiated via numerical simulations. Global sensitivity analysis identifies the important parameters having a significant impact on the fish population. The Partial Rank Correlation Coefficients (PRCCs) values of fish population in the lake with respect to input parameters of the system show that the growth rate of humans in the lake watershed has maximum negative correlation while the growth in the fish population due to DO has maximum positive correlation with the density of fish population in the lake. The results show that increase in human population may decrease fish population in the system to very low values. However, by controlling additional dissolved organic loads coming from domestic sewage, farm waste and many other sources, the level of DO can be brought back to values that allow fish survival. Maintaining it at these levels would preserve the ecosystem.

中文翻译：

---

人口对乌苏尔湖鱼类生存的影响

在本文中，我们介绍了一个模型来研究人口对水生介质中鱼类生存的影响。直接地，这是通过钓鱼发生的。间接地，这与导致有机污染的其他人类行为有关，从而导致溶解氧 (DO) 水平低，从而损害水生动物群。在数学上，我们考虑了涉及人口、有机污染物、细菌、溶解氧和鱼类种群的各种非线性过程。在本研究中，我们的目的是研究 DO 的消耗水平对这种水生系统中鱼类种群生存的影响。正在考虑的案例研究以印度班加罗尔的 Ulsoor 湖为代表。大量污水排入其中，导致溶解氧水平降低，鱼类大量死亡。分析平衡的可行性和稳定性，通过数值模拟证实。全球敏感性分析确定了对鱼类种群有重大影响的重要参数。湖中鱼类种群相对于系统输入参数的偏秩相关系数 (PRCCs) 值表明，湖泊流域内人类的增长率负相关最大，而 DO 引起的鱼类种群增长最大与湖中鱼类种群密度呈正相关。结果表明，人口的增加可能会使系统中的鱼类数量减少到非常低的值。然而，通过控制来自生活污水、农场废物和许多其他来源的额外溶解有机负荷，可以将溶解氧的水平恢复到允许鱼类生存的值。