# Chronic Inflammation in the Epidermis: A Mathematical Model
## 1 Introduction  
The skin is the largest tissue, which is composed of several different layers. The epidermis is located at the outmost part of the skin tissue, which acts as a first barrier for the invasion of physical (water), chemical (proteins) and biological (virus and bacteria) agents. A population of keratinocytes is the major cell type in the epidermis, which constitutes stratum basale, stratum spinosum, stratum granulosum and stratum corneum. Keratinocytes release anti-microbial peptides or pro-inflammatory cytokines to prevent bacterial or viral infection [1]. The second outmost layer, the dermis, is situated between the epidermis and subcutaneous tissues, which are composed of fibroblasts, macrophages and adipocytes [2]. The dermis contains extracellular matrix components,including collagen and elastin, as well as lymph, blood vessels and many skin-resident immune cell types. The homeostasis of the skin tissue is maintained by appropriate elimination of invading agents and tight regulation of cellular activities. On the other hand, the breakdown of the homeostasis of the skin tissue induces numerous diseases, including cancer, complications after an injury and inflammatory symptoms. Atopic dermatitis (AD) is one of the major skin inflammatory diseases, which are characterized by the elevated level of serum IgE and chronic allergic immune responses [3]. Incidence of AD has been increasing in developed countries. Notably, recent genetic studies have revealed that barrier dysfunction of the epidermis due to filaggrin mutation is a major triggering factor of disease progression [4; 5]. Filaggrin is synthesized in keratinocytes at the stratum granulosa, which is degraded to become a major component of natural moisturizing factor (NMF). Lack of NMFs is associated with water loss skin dryness, leading to the progression of AD and ichthyosis vulgaris [4]. Not only dry condition, but also excessive proteolytic activities of the epidermis are implicated as causal factors of AD. Patients with Netherton syndrome who exhibit atopic dermatitis-like chronic inflammation indicate a genetic defect causing excessive serine proteases [6]. The inference of bacteria as an environmental factor has been implicated as a possible factor for the progression of skin inflammatory diseases. Two major pathogenic bacteria species for skin diseases are _Staphylococcus aureus_ (_S. aureus_) and _Streptococcus pyogenes_ (_S. pyogenes_). Importantly, _S. aureus_ is a major virulent species, which is implicated to be associated with the progression of atopic dermatitis [7]. _S. aureus_ also induces impetigo and another serious symptoms. Methicillin-resistant _S. aureus_ (MRSA) is an antibiotic-resistant strain of _S. aureus_, the incidence of which is often reported as a nosocomial infection [8]. On the other hand, some commensal bacteria can exhibit mutualistic behaviors through the suppression of potentially pathogenic bacterial species via direct and indirect interactions, known as probiotic effects. For instance, _Staphylococcus epidermidis(S. epidermidis)_, a major commensal bacterial species in the skin, can support the host defense by releasing antimicrobial peptides [9; 10]. The other beneficial microbial species include species belonging to the _Lactobacillus_ genus. _Lactobacillus reuteri_ helps keratinocyte survival from _S. aureus_-induced cell death by outcompeting _S. aureus_[11]. The immune system plays a major role in preventing the invasion of numerous agents, including bacteria, fungi, virus and foreign proteins [12]. Not only foreign antigens, but also antigens presented by commensal bacteria can be an antigenic stimulation for the host immune system [13]. In fact, the number of bacteria in abundance is controlled by the host immune system under normal conditions [14]. The pathogenicity of _S. aureus_ can be conferred by numerous immune evasion strategies. In fact, several virulent factors of _S. aureus_ have been reported in [15; 16; 17]. On the contrary, several beneficial roles of _S.