Global dynamics of an epidemiological model with age of infection and disease relapse

Abnormal DNA methylation patterns in patients with infection‑caused leukocytopenia based on methylation microarrays

The present study aimed to investigate the association between gene methylation and leukocytopenia from the perspective of gene regulation. A total of 30 patients confirmed as having post-infection leukocytopenia at People's Hospital of Xinjiang Uygur Autonomous Region between January 2016 and June 2017 were successively recruited as the leukocytopenia group; 30 patients with post-infection leukocytosis were enrolled as the leukocytosis group. In addition, 30 healthy volunteers who received a health examination at the hospital during the same period were included as the normal control group. In each group, four individuals were randomly selected for whole genome methylation screening. After selection of key methylation sites, the remaining samples in each group were used for verification using matrix-assisted laser desorption/ionization-time of flight mass spectrometry. The levels of serum complement factors C3 and C5 in the leukocytopenia group were significantly lower than those in the other two groups (P<0.05). According to whole-genome DNA methylation detection, 66 and 27 methylation loci may be associated with leukocytopenia and leukocytosis, respectively. Most of these abnormal loci are located on chromosomes 2, 6, 7, 1, 17 and 11. The rates of WW domain containing E3 ubiquitin protein ligase 2 gene methylation at cytosine-phosphate-guanine (CpG)_1, CpG_5/6 and CpG_7 in the leukocytopenia group were higher than in the other two groups (P<0.05); the rate of AKT2 CpG_1 methylation was higher in the leukocytopenia group than in the other two groups (P<0.05); the rate of calcium-binding atopy-related autoantigen 1 gene CpG_2 methylation was higher in the leukocytosis group than in the normal control group (P<0.05); and the rate of NADPH oxidase 5 gene CpG_3 methylation was higher in the leukocytosis group than in the normal control group (P<0.05). Chemotactic factor secretion and cell migration abnormalities, ubiquitination modification disorders and reduced oxidative burst may participate in infection-complicated leukocytopenia. The results of this study shed new light on the molecular biological mechanisms of infection-complicated leukocytopenia and provide novel avenues for diagnosis and treatment.

Global dynamics of a tuberculosis model with fast and slow progression and age-dependent latency and infection

In this paper, a mathematical model describing tuberculosis transmission with fast and slow progression and age-dependent latency and infection is investigated. It is assumed in the model that infected individuals can develop tuberculosis by either of two pathogenic mechanisms: direct progression or endogenous reactivation. It is shown that the transmission dynamics of the disease is fully determined by the basic reproduction number. By analyzing corresponding characteristic equations, the local stability of a disease-free steady state and an endemic steady state of the model is established. By using the persistence theory for infinite dimensional system, it is proved that the system is uniformly persistent when the basic reproduction number is greater than unity. By constructing suitable Lyapunov functionals and using LaSalle's invariance principle, it is verified that the global dynamics of the system is completely determined by the basic reproduction number.