Permanence And Existence Of A Positive Periodic Solution To A Periodic Stage-Structured System With In Infinite Delay

In this paper we consider a periodic non-autonomous competitive stage-structured system with infinite delay for the interaction between n species, the adult members of which are in competition. For each of the n species the model incorporates a time delay which represents the time from birth to maturity of that species. Infinite delay is introduced which denotes the influential effect of the entire past history of the system on the current competition interactions. We first prove by using the comparison principle that if the growth rates are sufficiently large then the solutions are uniformly permanent. Then by using Horn's fixed point Theorem, we show that the system with finite delay has a positive periodic solution. As a consequence of this result, we prove that even the system with infinite delay admits a positive periodic solution

A mathematical model of HIV-1 infection including the saturation effect of healthy cell proliferation

In this paper we derive a model describing the dynamics of HIV-1 infection in tissue culture where the infection spreads directly from infected cells to healthy cells trough cell-to-cell contact. We assume that the infection rate between healthy and infected cells is a saturating function of cell concentration. Our analysis shows that if the basic reproduction number does not exceed unity then infected cells are cleared and the disease dies out. Otherwise, the infection is persistent with the existence of an infected equilibrium. Numerical simulations indicate that, depending on the fraction of cells surviving the incubation period, the solutions approach either an infected steady state or a periodic orbit

Toxoplasma gondii infection triggers chronic cachexia and sustained commensal dysbiosis in mice.

Toxoplasma gondii is a protozoan parasite with a predation-mediated transmission cycle between rodents and felines. Intermediate hosts acquire Toxoplasma by eating parasite cysts which invade the small intestine, disseminate systemically and finally establish host life-long chronic infection in brain and muscles. Here we show that Toxoplasma infection can trigger a severe form of sustained cachexia: a disease of progressive lean weight loss that is a causal predictor of mortality in cancer, chronic disease and many infections. Toxoplasma cachexia is characterized by acute anorexia, systemic inflammation and loss of 20% body mass. Although mice recover from symptoms of peak sickness, they fail to regain muscle mass or visceral adipose depots. We asked whether the damage to the intestinal microenvironment observed at acute time points was sustained in chronic infection and could thereby play a role in sustaining cachexia. We found that parasites replicate in the same region of the distal jejunum/proximal ileum throughout acute infection, inducing the development of secondary lymphoid structures and severe, regional inflammation. Small intestine pathology was resolved by 5 weeks post-infection. However, changes in the commensal populations, notably an outgrowth of Clostridia spp., were sustained in chronic infection. Importantly, uninfected animals co-housed with infected mice display similar changes in commensal microflora but never display symptoms of cachexia, indicating that altered commensals are not sufficient to explain the cachexia phenotype alone. These studies indicate that Toxoplasma infection is a novel and robust model to study the immune-metabolic interactions that contribute to chronic cachexia development, pathology and potential reversal