Solutions for certain classes of Riccati differential equation

We derive some analytic closed-form solutions for a class of Riccati equation y'(x)-\lambda_0(x)y(x)\pm y^2(x)=\pm s_0(x), where \lambda_0(x), s_0(x) are C^{\infty}-functions. We show that if \delta_n=\lambda_n s_{n-1}-\lambda_{n-1}s_n=0, where \lambda_{n}= \lambda_{n-1}^\prime+s_{n-1}+\lambda_0\lambda_{n-1} and s_{n}=s_{n-1}^\prime+s_0\lambda_{k-1}, n=1,2,..., then The Riccati equation has a solution given by y(x)=\mp s_{n-1}(x)/\lambda_{n-1}(x). Extension to the generalized Riccati equation y'(x)+P(x)y(x)+Q(x)y^2(x)=R(x) is also investigated.Comment: 10 page

Solvable Systems of Linear Differential Equations

The asymptotic iteration method (AIM) is an iterative technique used to find exact and approximate solutions to second-order linear differential equations. In this work, we employed AIM to solve systems of two first-order linear differential equations. The termination criteria of AIM will be re-examined and the whole theory is re-worked in order to fit this new application. As a result of our investigation, an interesting connection between the solution of linear systems and the solution of Riccati equations is established. Further, new classes of exactly solvable systems of linear differential equations with variable coefficients are obtained. The method discussed allow to construct many solvable classes through a simple procedure.Comment: 13 page

Workshop 1: Surveillance issues of pandemic influenza

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Vaccine-Associated Enhanced Respiratory Disease Does Not Interfere with the Adaptive Immune Response Following Challenge with Pandemic A/H1N1 2009

The implications of sequential prime and challenge with mismatched influenza A viruses is a concern in mammals, including humans. We evaluated the ability of pigs affected with vaccine-associated enhanced respiratory disease (VAERD) to generate a humoral immune response against the heterologous challenge virus inciting the VAERD. Vaccinated and challenged (V/C) pigs were administered an inactivated swine δ-cluster H1N2 (MN08) vaccine with an HA similar to pre-2009 seasonal human viruses and challenged with heterologous A(H1N1) pandemic 2009 (H1N1pdm09). Vaccination induced MN08-specific hemagglutination inhibition (HI) antibody but not cross-reacting H1N1pdm09 HI antibody. However, vaccinated pigs demonstrated significantly higher post-challenge anti-H1N1pdm09 serum neutralizing (SN) antibodies at 14 and 21 days post inoculation (dpi) compared to nonvaccinated, challenged pigs (NV/C), indicating a priming effect of the vaccine. Serum and lung whole virus anti-H1N1pdm09 IgG ELISA antibodies in the vaccinated group were significantly higher than the challenge only pigs at all-time points evaluated. Lung IgA ELISA antibodies to both antigens were detected at 2, 5, and 21 dpi in vaccine-primed pigs, contrasted against mucosal ELISA antibody responses detected only at 21 dpi in the naïve-challenged group. Collectively, vaccine-primed pigs demonstrated a robust humoral immune response and elevated local adaptive cytokine levels, indicating VAERD does not adversely affect the induction of an immune response to challenge with heterologous virus despite the severe clinical disease and underlying lung pathology. Thus, original antigenic sin does not appear to be a component of VAERD.This article is from Viral Immunology 26 (2013): 314, doi:10.1089/vim.2013.0018.</p

CD28null CD4 T-cell expansions in autoimmune disease suggest a link with cytomegalovirus infection

Immunosenescence is thought to contribute to the increase of autoimmune diseases in older people. Immunosenescence is often associated with the presence of an expanded population of CD4 T cells lacking expression of CD28 (CD28null). These highly cytotoxic CD4 T cells were isolated from disease-affected tissues in patients with rheumatoid arthritis, systemic lupus erythematosus, multiple sclerosis, or other chronic inflammatory diseases and their numbers appeared to be linked to disease severity. However, we recently demonstrated that the common herpes virus, cytomegalovirus (CMV), not ageing, is the major driver of this subset of cytotoxic T cells. In this review, we discuss how CMV might potentiate and exacerbate autoimmune disease through the expansion of CD28null CD4 T cells