A Model for SARS-CoV-2 Infection with Treatment.

The current emergence of coronavirus (SARS-CoV-2) puts the world in threat. The structural research on the receptor recognition by SARS-CoV-2 has identified the key interactions between SARS-CoV-2 spike protein and its host (epithelial cell) receptor, also known as angiotensin-converting enzyme 2 (ACE2). It controls both the cross-species and human-to-human transmissions of SARS-CoV-2. In view of this, we propose and analyze a mathematical model for investigating the effect of CTL responses over the viral mutation to control the viral infection when a postinfection immunostimulant drug (pidotimod) is administered at regular intervals. Dynamics of the system with and without impulses have been analyzed using the basic reproduction number. This study shows that the proper dosing interval and drug dose both are important to eradicate the viral infection.

Modelling the Effect of Incubation and Latent Periods on the Dynamics of Vector-Borne Plant Viral Diseases.

Most of the plant viral diseases spread through vectors. In case of the persistently transmitted disease, there is a latent time of infection inside the vector after acquisition of the virus from the infected plant. Again, the plant after getting infectious agent shows an incubation time after the interaction with an infected vector before it becomes diseased. The goal of this work is to study the effect of both incubation delay and latent time on the dynamics of plant disease, and accordingly a delayed model has been proposed. The existence of the equilibria, basic reproductive number ([Formula: see text]) and stability of equilibria have been studied. This study shows the relevance of the presence of two time delays, which may lead to system stabilization.

A vivid cytokines interaction model on psoriasis with the effect of impulse biologic (TNF-α inhibitor) therapy.

Psoriasis is a chronic skin condition that produces plaques of condensed, scaling skin due to excessively rapid proliferation of keratinocytes. During the disease progression, keratinocyte proliferation is influenced by many immune cells and cytokines. This article deals with a five dimensional deterministic model, which has been derived using quasi-steady-state approximation for describing the dynamics of psoriasis in various cytokines environment. Equilibrium analysis of the system shows that either the system converges to a stable steady state or exhibits a periodic oscillation depending upon system parameters. Finally, introducing a one dimensional impulsive system, we have determined the perfect dose and perfect dosing interval for biologic (TNF-α inhibitor) therapy to control the hyper-proliferation of keratinocytes. We have studied the effect of TNF-α inhibitor by considering both perfect and imperfect dosing during the inductive phase. The maximum possible number of drug holidays and the minimal number of doses that must subsequently be taken while avoiding drug resistance have been calculated for imperfect dosing. Since, psoriasis is non-curable but treatable disease, so the aim is to investigate the minimum dose with highest efficacy and proper dosing interval of TNF-α inhibitor for a psoriatic patient. Through numerical simulations, we have given a detailed prediction about the maximum drug holidays, tolerable for a patient, without loss of previous drug effects. Our theoretical predictions and numerical outcomes may be useful in guiding the design of future clinical trials.