Human immunodeficiency virus/acquired immune deficiency syndrome: Using drug from mathematical perceptive

Critical observation of WHO recommended multidrug therapy on the disease leprosy through mathematical study

Leprosy is a skin disease and it is characterized by a disorder of the peripheral nervous system which occurs due to the infection of Schwann cells. In this research article, we have formulated a four-dimensional ODE-based mathematical model which consists of the densities of healthy Schwann cells, infected Schwann cells, M. leprae bacteria, and the concentration of multidrug therapy (MDT). This work primarily aims on exploring the dynamical changes and interrelations of the system cell populations during the disease progression. Also, evaluating a critical value of the drug efficacy rate of MDT remains our key focus in this article so that a safe drug dose regimen for leprosy can be framed more effectively and realistically. We have examined the stability scenario of different equilibria and the occurrence of Hopf-bifurcation for the densities of our system cell populations with respect to the drug efficacy rate of MDT to gain insight on the precise impact of the efficiency rate on both the infected Schwann cell and the bacterial populations. Also, a necessary transversality condition for the occurrence of the bifurcation has been established. Our analytical and numerical investigations in this research work precisely explores that the process of demyelination, nerve regeneration, and infection of the healthy Schwann cells are the three most crucial factors in the leprosy pathogenesis and to control the M. leprae-induced infection of Schwann cells successfully, a more flexible version of MDT regime with efficacy rate varying in the range η∈(0.025,0.059) for 100-120 days in PB cases and 300 days in MB cases obtained in this research article should be applied. All of our analytical outcomes have been verified through numerical simulations and compared with some existing clinical findings.

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.

MODELING MONOCYTE-DERIVED DENDRITIC CELLS AS A THERAPEUTIC VACCINE AGAINST HIV

Successful immunologic control of HIV infection can be achieved in long-term non-progressors or HIV-1 controllers. Dendritic cells (DCs) are required for specific antigen presentation to naïve T lymphocytes and for antiviral, type I interferon secretion. To understand this mechanism, we develop a mathematical model that describes the role of direct presentation (replicating virus-infected DCs or other [Formula: see text] T cells directly) and cross presentation (DCs obtain antigen processed in other infected cells such as [Formula: see text] T lymphocytes) during HIV-1 infection. We find equilibria and determine stability in the case of no vaccination, and then, when vaccination is taken, we determine analytical thresholds for the strength and frequency of the vaccine to ensure the disease-free equilibrium remains stable. Our theoretical results suggest that the restoration of DC numbers may be predictive of immune restoration and may be a goal for immunotherapy to enhance viral control in a larger proportion of patients.