Abstract
In this literature, we probe a stochastic host-pathogen tuberculosis model with the adaptive immune response of four states of epidemiological classification: Mycobacterium tuberculosis, uninfected macrophages, infected macrophages, and immune response CD4+ T cells. This model is pertinent to the latent stage of tuberculosis infection and active tuberculosis-infected individuals. The stochastic host-pathogen tuberculosis model in pathology is constituted based on the environmental influence on the Mycobacterium tuberculosis and macrophage population, elucidated by stochastic perturbations, and it is proportional to each state. We evince the existence and a unique global positive solution of a stochastic tuberculosis model. We attain sufficient conditions for the extinction of the tubercle bacillus. Moreover, we acquire the existence of the stationary distribution of the positive solutions by the Lyapunov function method. Eventually, numerical simulations validate analytical findings and the dynamics of the stochastic TB model.
Highlights
In the annals of history, there have been many threats such as natural calamity, diseases, and wild animals for the existence of humans; among these, diseases seem to be the main cause of death
Mycobacterium tuberculosis (MTB)-specific CD4+ 1 cell response is recognized as possessing a protective role for the power to generate cytokines such as INF-c and tumour necrosis factor-α (TNF-α) that involve the processes of recruitment and activation of innate immune cells as monocytes and granulocytes
Based on the above factors, we put forth the stochastic hostpathogen TB model with adaptive immune response. e stochastic host-pathogen TB model on the basis of the influence of the environment on the Mycobacterium tuberculosis and macrophage population was manifested by stochastic perturbations and it is proportional to each state [38, 39]
Summary
In the annals of history, there have been many threats such as natural calamity, diseases, and wild animals for the existence of humans; among these, diseases seem to be the main cause of death. MTB-specific CD4+ 1 cell response is recognized as possessing a protective role for the power to generate cytokines such as INF-c and TNF-α that involve the processes of recruitment and activation of innate immune cells as monocytes and granulocytes. In this way, when other antigen-specific T cells such as CD8+ cells [14], natural killer (NK) cells, cδT cells, nonclassical (MHC) class I molecule CD1, controlled T cells are able to raise INF-c during MTB infection and they are unable to equalize the lack of CD4+ T cells.
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