A MODEL OF THE OPTIMAL IMMUNOTHERAPY OF PSORIASIS BY INTRODUCING IL-10 AND IL-22 INHIBITORS

Psoriasis is a chronic skin disease in which the process of hyper-proliferation (excessive division) of skin cells starts. Externally, psoriasis appears as red papules, on the surface of which there are scales of white–gray color. There is substantial evidence that T-helper cells take vital accountability for creating the hyper-proliferation of keratinocytes (skin cells), which causes itching of skin patches. In this paper, we propose a mathematical model describing the concentrations of T-helper and keratinocyte cell populations to predict cellular behaviors for psoriasis regulation under normal or anomalous immune circumstances. Local and global asymptotic stabilities of the model equilibria are investigated. Additionally, by introducing two scalar bounded controls into the model, the effect of combined immunotherapy using IL-10 and IL-22 inhibitors is analyzed. The optimal control problem of minimizing the cost of immune therapy and simultaneous optimizing the effect of this therapy on T-helper cells and keratinocytes proliferation is formulated and solved by applying the Pontryagin maximum principle. Within the restrictions of the proposed model, the obtained analytical and numerical outcomes suggest that the optimal strategy of injecting IL-10 and IL-22 inhibitors can be effective for psoriasis treatment.

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.

A MATHEMATICAL MODEL ON CTL MEDIATED CONTROL OF HIV INFECTION IN A LONG-TERM DRUG THERAPY

Bonhoeffer et al.1studied the long-term dynamics of HIV drug therapy and virus load dynamics. It is well known that highly active anti retroviral therapy (HAART) can effectively control the HIV replication. It is also well known that reverse transcriptase inhibitors (RTIs) could block new infection and as a result control HIV infection. The positive feedback control on such dynamics plays an important role and CD4+T cells are not only produced from a source but also produced from existing T cells. The present investigation takes into account these factors in the original model of Bonhoeffer et al. The optimal control therapy and the effect of time delay in the positive feedback control function have been investigated. Numerical simulation of the nonlinear model has confirmed our analytical studies.

SATURATION EFFECTS FOR CTL MEDIATED CONTROL OF HIV-1 INFECTION: A MATHEMATICAL STUDY

The relations between the Human Immunodeficiency Virus-1 (HIV-1) and the human immune system are astonishingly multifaceted, where the critical role for cytotoxic T lymphocytes (CTLs) in the suppression of viral replication in HIV-1 infected individuals cannot be ignored. In this research paper, we have proposed a mathematical model incorporating half saturation constant through the CTL mediated killing process and also in that sense, it has been infiltrated in the generation process of CTL through infected cells. To make the model more realistic, a time lag is introduced in the generation term of CTL population. Also an optimal control theory paradigm is used in our mathematical model to suppress the viral production. From our entire analysis, we have found threshold condition of half saturation constant and treatment schedule so that we can handle the situation of Acquired Immunodeficiency Syndrome (AIDS) patients in a better way. Our analysis reveals that, if the half saturation constant is around 47 mm-3in the saturation process and the drug therapy is to be used around 76 days, then we can get adequate results for better treatment of a HIV-1 patient. Based on numerical results, we observed that in a highly unstable situation, administration of chemotherapy at a high dose can stabilize the system.