A model analysis to measure the adherence of Etanercept and Fezakinumab therapy for the treatment of psoriasis

This article deals with a immunological model, which includes multiple classes of T cells, namely, the naive T cell, type I, type II and type 17 T helper cells (Th1, Th2, Th17), regulatory T cell (Treg) along with the activated natural killer cells (NK cells) and epidermal keratinocytes. In order to describe the etiology of psoriasis development, we have studied the basic mathematical properties of the model, existence and stability of the interior equilibrium. We have also derived the drug-induced mathematical model using impulse differential equation to determine the effects of combined biologics Etanercept (TNF-α inhibitor) and Fezakinumab (IL-22 monoclonal antibody) therapy considering perfect dosing during the inductive phase. We have determined the required dosing interval of both drugs to maintain the keratinocytes concentration below a threshold level. This study shows that Etanercept alone could theoretically maintain the keratinocytes level, whereas frequent dosing of Fezakinumab alone may not be enough to control the hyper-proliferation of keratinocytes. Furthermore, combination of the drugs with perfect dosing has the noticeable effect on keratinocytes dynamics, which may be suitable therapeutic approaches for treatment of psoriasis

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

Long term dynamics in a mathematical model of HIV-1 infection with delay in different variants of the basic drug therapy model

Infection with HIV-1, degrading the human immune system and recent advances of drug therapy to arrest HIV-1 infection, has generated considerable research interest in the area. Sebastian Bonhoeffer et al. [2], introduced a population model representing long term dynamics of HIV infection in response to available drug therapies. We consider a similar type of approximate model incorporating time delay in the process of infection on the healthy T cells which, in turn, implies inclusion of a similar delay in the process of viral replication. The model is studied both analytically and numerically. We also include a similar delay in the killing rate of infected CD4+ T cells by Cytotoxic TLymphocyte (CTL) and in the stimulation of CTL and analyze two resulting models numerically. The models with no time delay present have two equilibria: one where there is no infection and a non-trivial equilibrium where the infection can persist. If there is no time delay then the non-trivial equilibrium is locally asymptotically stable. Both our analytical results (for the first model) and our numerical results (for all three models) indicate that introduction of a time delay can destabilize the non-trivial equilibrium. The numerical results indicate that such destabilization occurs at realistic time delays and that there is a threshold time delay beneath which the equilibrium with infection present is locally asymptotically stable and above which this equilibrium is unstable and exhibits oscillatory solutions of increasing amplitude

Numerical prediction of flow and heat transfer characteristics of water-fly ash slurry in a 180° return pipe bend

A three-dimensional numerical simulation is performed to predict the thermofluidic transport characteristics of water-fly ash slurry in an 180° return bend. U pipelines of diameter 53 mm with radius ratios of 2.98 and 5.6 are considered that may replicate a shell and tube type heat exchanger. The pressure drop and heat transfer characteristics are predicted and the effects of Dean, Nusselt and Reynolds numbers on the vortex structure formation and heat transfer are studied. The numerical simulation is carried out by deploying the granular Eulerian multiphase model following a finite volume approach. The turbulent transport is addressed using the RNG turbulence model. The results revealed that the heat transfer coefficient of pipe bends of smaller radius ratio is 53.28% more than the larger radius ratio for the solid concentration of 10% and velocity of 1 m/s. Its value increases with increase in the particle concentration and velocity due to the presence of a secondary flow in the bends. The Dean number increases with decreasing the radius ratio and the average Nusselt number increases with increasing the Reynolds number. With increasing Dean Number, the Nusselt number increases with decreasing the radius of curvature for the same particle concentration. When the particle concentration increases, the average Nusselt number also increases. The average Nusselt number in the return bend appears to be higher than that in the inlet and outlet pipes due to the presence of the secondary flows

Effect of Antiviral Therapy for HCV Treatment in the Presence of Hepatocyte Growth Factor

The effect of antiviral therapy during Hepatitis C Virus (HCV) infection is the focus of this study. HCV infection destroys healthy hepatocyte cells in the human liver, causing cirrhosis and hepatocellular carcinoma. We introduce a cell-population model representing the long-term dynamics of HCV infection in response to antiviral drug therapies. The proliferation of existing cells can create hepatocyte cells in the system. Such models are based on the dynamics of susceptible hepatocytes, infected hepatocytes and HCV with interactive dynamics, which can give a complete understanding of the host dynamics of the system in the presence of antiviral drug therapy. Infection-free equilibrium and endemic equilibrium are two equilibrium states in the absence of drugs. The existence and stability conditions for both systems are presented. We also construct an optimal control system to find the optimal control strategy. Numerical results show that the effects of the proliferation rate and infection rate are critical for the changes in the dynamics of the model. The impact of different weight factors on the optimal control problem is analysed through numerical simulation

Effect of Antiviral Therapy for HCV Treatment in the Presence of Hepatocyte Growth Factor

The effect of antiviral therapy during Hepatitis C Virus (HCV) infection is the focus of this study. HCV infection destroys healthy hepatocyte cells in the human liver, causing cirrhosis and hepatocellular carcinoma. We introduce a cell-population model representing the long-term dynamics of HCV infection in response to antiviral drug therapies. The proliferation of existing cells can create hepatocyte cells in the system. Such models are based on the dynamics of susceptible hepatocytes, infected hepatocytes and HCV with interactive dynamics, which can give a complete understanding of the host dynamics of the system in the presence of antiviral drug therapy. Infection-free equilibrium and endemic equilibrium are two equilibrium states in the absence of drugs. The existence and stability conditions for both systems are presented. We also construct an optimal control system to find the optimal control strategy. Numerical results show that the effects of the proliferation rate and infection rate are critical for the changes in the dynamics of the model. The impact of different weight factors on the optimal control problem is analysed through numerical simulation

Hopf bifurcation and optimal control of HCV/HIV co-infection dynamics within human: A theoretical study

Pathogen and human host interaction dynamics are often more complicated in the presence of co-pathogens. Co-infection can occur either as the presence of pre-existing pathogen which is accelerated by the new pathogen and more complications happened. In this study, we look at the burden of HIV/HCV viremia and the efficacy of treatment in reducing the severity of HIV/HCV co-infection patterns. Disease-free equilibrium and endemic equilibrium are two equilibrium states determined in the absence of drugs. The basic reproduction number is computed and the stability of the disease-free equilibrium of the model is analyzed using it. Here we have also incorporated the optimal drug therapy to control the co-infection disease progression. The efficacy of treatment has also been found to influence the natural progression of HCV in HIV/HCV co-infection. The numerical results suggest that the HIV viral load impacts the severity of the HCV infection impressively. This research is significant to develop antiviral therapy strategies to control HIV/HCV co-infection. The most effective way to control the co-infection with the minimum side effects is to take the combination of three medications with optimal dosing

A Fractional-Order Compartmental Model of Vaccination for COVID-19 with the Fear Factor

During the past several years, the deadly COVID-19 pandemic has dramatically affected the world; the death toll exceeds 4.8 million across the world according to current statistics. Mathematical modeling is one of the critical tools being used to fight against this deadly infectious disease. It has been observed that the transmission of COVID-19 follows a fading memory process. We have used the fractional order differential operator to identify this kind of disease transmission, considering both fear effects and vaccination in our proposed mathematical model. Our COVID-19 disease model was analyzed by considering the Caputo fractional operator. A brief description of this operator and a mathematical analysis of the proposed model involving this operator are presented. In addition, a numerical simulation of the proposed model is presented along with the resulting analytical findings. We show that fear effects play a pivotal role in reducing infections in the population as well as in encouraging the vaccination campaign. Furthermore, decreasing the fractional-order parameter α value minimizes the number of infected individuals. The analysis presented here reveals that the system switches its stability for the critical value of the basic reproduction number R0=1