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Register a new userDynamics of tritrophic interaction with volatile compounds in plants
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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 positivity and boundedness of the system solutions, existence of positive equilibrium and its local stability, we analyse global stability of positive equilibrium via the geometrical approach of Li and Muldowney. We pay attention to parameters in order to discuss different types of bifurcations. Finally, we present some numerical simulations to justify our analytical results.
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While many epidemiological models have being proposed to understand and handle COVID-19, too little has been invested to understand how the virus replicates in the human body and potential antiviral can be used to control the replication cycle. In this work, using a control theoretical approach, validated mathematical models of SARS-CoV-2 in humans are properly characterized. A complete analysis of the main dynamic characteristic is developed based on the reproduction number. The equilibrium regions of the system are fully characterized, and the stability of such a regions, formally established. Mathematical analysis highlights critical conditions to decrease monotonically SARS-CoV-2 in the host, such conditions are relevant to tailor future antiviral treatments. Simulation results show the potential benefits of the aforementioned system characterization.
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Mathematical models describing SARS-CoV-2 dynamics and the corresponding immune responses in patients with COVID-19 can be critical to evaluate possible clinical outcomes of antiviral treatments. In this work, based on the concept of virus spreadability in the host, antiviral effectiveness thresholds are determined to establish whether or not a treatment will be able to clear the infection. In addition, the virus dynamic in the host -- including the time-to-peak and the final monotonically decreasing behavior -- is chracterized as a function of the treatment initial time. Simulation results, based on nine real patient data, show the potential clinical benefits of a treatment classification according to patient critical parameters. This study is aimed at paving the way for the different antivirals being developed to tackle SARS-CoV-2.
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