A mathematical insight to control the disease psoriasis using mesenchymal stem cell transplantation with a biologic inhibitor

Psoriasis is a chronic, non-contagious, immune-mediated skin disorder. Inflammation of the skin's surface is characterised by scaly white, red, or silvery spots that occur due to the hyper-proliferation of keratinocytes in the epidermal layer. Primarily, pharmaceutical drugs or immune therapy are used to treat psoriasis. We are all aware that, certain therapeutic strategies can have some adverse effects, and over time, that hidden inflammation may manifest. This article introduces a mathematical model for psoriasis, formulated by employing a set of nonlinear ordinary differential equations (ODEs) that describe the densities of T-cells, dendritic cells (DCs), keratinocytes, and mesenchymal stromal cells (MSCs) as basic cell populations. A tumor necrosis factor- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math> ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>T</mml:mi> <mml:mi>N</mml:mi> <mml:mi>F</mml:mi> <mml:mo>-</mml:mo> <mml:mi>α</mml:mi></mml:mrow> </mml:math> ) inhibitor has been imposed from the initial stage of the treatment regime, using the optimal control theoretic approach, and the numerical results have been observed. After 80 days of monitoring using only biologic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>T</mml:mi> <mml:mi>N</mml:mi> <mml:mi>F</mml:mi> <mml:mo>-</mml:mo> <mml:mi>α</mml:mi></mml:mrow> </mml:math> inhibitors, if this approach did not provide the intended outcomes (when severity arises), stem cells are administered a few times in a pulsed manner as a cell replacement technique in addition to this anti <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>T</mml:mi> <mml:mi>N</mml:mi> <mml:mi>F</mml:mi> <mml:mo>-</mml:mo> <mml:mi>α</mml:mi></mml:mrow> </mml:math> medicine. We have observed the combined therapeutic benefit of stem cell replacement with a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>T</mml:mi> <mml:mi>N</mml:mi> <mml:mi>F</mml:mi> <mml:mo>-</mml:mo> <mml:mi>α</mml:mi></mml:mrow> </mml:math> inhibitor from a mathematical point of view. The theoretical analysis and the numerical results revealed that stem cell transplantation, along with a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>T</mml:mi> <mml:mi>N</mml:mi> <mml:mi>F</mml:mi> <mml:mo>-</mml:mo> <mml:mi>α</mml:mi></mml:mrow> </mml:math> inhibitor, is a promising psoriasis treatment option moving forward.