Effect of CD4+ T-Cells and CD8+ T-Cells on Psoriasis: a mathematical study

Paper presented at the 3rd Strathmore International Mathematics Conference (SIMC 2015), 3 - 7 August 2015, Strathmore University, Nairobi, Kenya.Psoriasis is a common chronic inflammatory skin disease that is differentiated by repeated occurrences of raised scaly and red skin plaques. It is generated through several applications of drugs, strains, physical wounds to the skin and also for infectivity. Psoriasis is identified by composite interactions of T-Cells, Dendritic Cells, Cytokines and downstream transcription factors (type 1 Cytokines network). The effects of T-Cells in dermal layer (CD4+ T-Cells) are well-studied in the disease dynamics of Psoriasis from mathematical as well as biological context. But the concept of T-Cells in epidermal layer (CD8+ T-Cells) for disease progression of Psori-asis has not yet been explored till now from mathematical avenue. Here we introduce both CD4+ and CD8+ T-Cell, Dendritic Cell and Keratinocyte population to notice the impact of them on immunopathogenic cell-biological mechanism of Psoriasis. Numerical simulation is also furnished to establish the analytical outcomes

Diffusion-driven instability and pattern formation in a prey-predator model with fear and Allee effect

This paper analyses a predator-prey model with Holling type II response function incorporating Allee and fear effect in the prey. The model includes intra species competition among predators. We find out the local dynamics as well as Hopf bifurcation by considering level of fear as bifurcation parameter. The condition for diffusion-driven instability and patterns are then demonstrated in relation to the system's ecological parameters and diffusion coefficients. Intra-specific competition affects the dynamics of the system and Turing pattern formation. Moreover, output of results is verified through numerical simulation. Thus, from a dynamical standpoint, the considered model seems to be relevant in the field of ecology