Research Article Bifurcation Analysis of a 5D Nutrient, Plankton, Limnothrissa miodon Model with Hydrocynus vittatus Predation Farikayi K. Mutasa , 1 Brian Jones, 2 Itai H. Tendaupenyu, 3 Tamuka Nhiwatiwa, 4 and Mzime R. Ndebele-Murisa 5 1 Department of Applied Mathematics, National University of Science and Technology, P.O. Box AC939, Ascot, Bulawayo, Zimbabwe 2 Department of Statistics and Operations Research, National University of Science and Technology, P.O. Box AC939, Ascot, Bulawayo, Zimbabwe 3 The Zimbabwe Parks and Wildlife Management Authority, Cnr Sandringham & Borrowdale Rd, Botanical Gardens, PO BOX CY140, Causeway Harare, Zimbabwe 4 Department of Biological Sciences, University of Zimbabwe, P.O. MP167 Mt. Pleasant, Harare, Zimbabwe 5 School of Wildlife and Ecology, Chinhoyi University of Technology, Chinhoyi, Zimbabwe Correspondence should be addressed to Farikayi K. Mutasa; farikayi.mutasa@nust.ac.zw Received 4 April 2022; Revised 29 June 2022; Accepted 1 July 2022; Published 20 July 2022 Academic Editor: Wei-Chiang Hong Copyright © 2022 Farikayi K. Mutasa et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this paper, we construct and analyze a theoretical, deterministic 5D mathematical model of Limnothrissa miodon with nutrients, phytoplankton, zooplankton, and Hydrocynus vittatus predation. Local stability analysis results agree with the numerical simulations in that the coexistence equilibrium is locally stable provided that certain conditions are satisfied. The coexistence equilibrium is globally stable if certain conditions are met. Existence, stability, and direction of Hopf bifurcations are derived for some parameters. Bifurcation analysis shows that the model undergoes Hopf bifurcation at the coexistence point for the zooplankton growth rate with periodic doubling leading to chaos. 1. Introduction Hydrocynus vittatus (Castelnau, 1861), also referred to as tigerfish, is the major predator of Limnothrissa miodon (Boulenger, 1906), also referred to as kapenta in Lake Kariba [1]. It is therefore important to investigate mathematically the role that tigerfish plays in the dynamics of Limnothrissa miodon. This paper begins by formulating and analyzing a deterministic Limnothrissa miodon model. The model has 5 classes, and these are as follows: concentration of nutrients, population density of phytoplankton, zooplankton popula- tion density, density of the Limnothrissa miodon population, and population density of tigerfish. The densities in each class are functions of time and are denoted by N ðt Þ, Pðt Þ, Zðt Þ, Lðt Þ, and Rðt Þ, respectively. The model is analyzed to determine the effect of predation on the population density of Limnothrissa miodon using qualitative techniques. Numerical simulations are done to illustrate the dynamics of the Limnothrissa miodon model. Mathematical modeling of the Limnothrissa miodon model with tigerfish predation will give us an insight into the dynamics of the kapenta fishery in Lake Kariba. A deterministic model that involves nutrients, phytoplankton, zooplankton, Limnothrissa miodon, and tigerfish has not been formulated and analyzed. In this paper, we formulate and analyze a deterministic, continuous, dynamical system which consists of ordinary differential equations that describe the dynamics of Limnothrissa miodon in the pres- ence of nutrients, phytoplankton, and zooplankton and with tigerfish predation. The Limnothrissa miodon model will help in our understanding of the dynamics of the aquatic ecosystem in the kapenta fishery in Lake Kariba. The major predator in Lake Kariba is tigerfish [2, 3], and after the introduction of Limnothrissa miodon into Lake Hindawi Journal of Applied Mathematics Volume 2022, Article ID 1095441, 21 pages https://doi.org/10.1155/2022/1095441