Dynamics of a virus-host model with an intrinsic quota. (English) Zbl 1217.37080

Summary: We develop and analyze a mathematical model describing the dynamics of infection by a virus of a host population in a freshwater environment. Our model, which consists of a system of nonlinear ordinary differential equations, includes an intrinsic quota, that is, we use a nutrient (e.g., phosphorus) as a limiting element for the host and potentially for the virus. Motivation for such a model arises from studies that raise the possibility that on the one hand, viruses may be limited by phosphorus, and on the other, that they may have a role in stimulating the host to acquire the nutrient. We perform an in-depth mathematical analysis of the system including the existence and uniqueness of solutions, equilibria, asymptotic, and persistence analysis. We compare the model with experimental data, and find that biologically meaningful parameter values provide a good fit. We conclude that the mathematical model supports the hypothesized role of stored nutrient regulating the dynamics, and that the coexistence of virus and host is the natural state of the system.


37N25 Dynamical systems in biology
92D30 Epidemiology
34D20 Stability of solutions to ordinary differential equations
Full Text: DOI


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