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We revisit the well-known chemostat model, considering that bacteria can be attached together in aggregates or flocs. We distinguish explicitly free and attached compartments in the model and give sufficient conditions for coexistence of these two forms. We then study the case of fast attachment and detachment and shows how it is related to density-dependent growth functions. Finally, we give some insights concerning the cases of multi-specific flocs and different removal rates.
Coronavirus disease 2019 (CoViD-19) is an infectious disease caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Among many symptoms, cough, fever and tiredness are the most common. People over 60 years old and with associated com
We propose a qualitative analysis of a recent fractional-order COVID-19 model. We start by showing that the model is mathematically and biologically well posed. Then, we give a proof on the global stability of the disease free equilibrium point. Fina
In this paper we provide the derivation of a super compact pairwise model with only 4 equations in the context of describing susceptible-infected-susceptible (SIS) epidemic dynamics on heterogenous networks. The super compact model is based on a new
Controlling pest insects is a challenge of main importance to preserve crop production. In the context of Integrated Pest Management (IPM) programs, we develop a generic model to study the impact of mating disruption control using an artificial femal
In this paper we will consider a mathematical model that describes, the tritrophic interaction between plants, herbivores and their natural enemies, where volatiles organic compounds (VOCs) released by plants play an important role. We show positivit