A novel mathematical model of AIDS-associated Kaposi's sarcoma: Analysis and optimal control.

Kaposi's sarcoma (KS) has been the most common HHV-8 virus-induced neoplasm associated with HIV-1 infection. Although the standard KS therapy has not changed in 20 years, not all cases of KS will respond to the same therapy. The goal of current AIDS-KS treatment modalities is to reconstitute the immune system and suppress HIV-1 replication, but newer treatment modalities are on horizon. There are very few mathematical models that have included HIV-1 viral load (VL) measures, despite VL being a key determinant of treatment outcome. Here we introduce a mathematical model that consolidates the effect of both HIV-1 and HHV-8 VL on KS tumor progression by incorporating low or high VLs into the proliferation terms of the immune cell populations. Regulation of HIV-1/HHV-8 VL and viral reservoir cells is crucial for restoring a patient to an asymptomatic stage. Therefore, an optimal control strategy given by a combined antiretroviral therapy (cART) is derived. The results indicate that the drug treatment strategies are capable of removing the viral reservoirs faster and consequently, the HIV-1 and KS tumor burden is reduced. The predictions of the mathematical model have the potential to offer more effective therapeutic interventions based on viral and virus-infected cell load and support new studies addressing the superiority of VL over CD4+ T-cell count in HIV-1 pathogenesis.

Preoperative Determinants of Patient-reported Pain and Physical Function Levels Following Total Knee Arthroplasty: A Systematic Review.

BACKGROUND: A sound knowledge of the determinants of total knee arthroplasty (TKA) outcomes could help in patient selection, preparation and education. We aimed to assess the current status of the literature evaluating preoperative determinants of early and medium term patient-reported pain and disability following TKA. METHOD: A search in Medline, Pubmed, Embase and CINAHL until October 2014 was undertaken. Selection criteria included: 1- participants undergoing primary unilateral TKA with a follow-up from 6 months to 2 years, 2- validated disease-specific patient-reported outcome measures assessing pain and/or function used as outcome measure and 3- identification of preoperative determinants obtained via multivariate analyses. Risk of bias was assessed using a modified version of the Methodology checklist for prognostic studies. RESULTS: Thirty-three prognostic explanatory studies were included. Mean total score of the methodological quality was 80.7±12.2 %. Sociodemographic and psychosocial determinants included greater socioeconomic deprivation (both studies), greater levels of depression and/or anxiety (7 out of 10 studies) and greater preoperative pain catastrophizing (all 3 studies). Significant clinical determinants included worse pre-operative knee related pain or disability (20 out of 22 studies), presence or greater levels of comorbidity (12 out of 23 studies), back pain (4 out of 5 studies) and lower general health (all 11 studies). CONCLUSION: Several significant determinants of short to medium-term pain and functional outcomes following TKA have been summarized by studies with moderate-to-high methodological quality. No conclusions can be reached regarding the strength of the associations between significant determinants and TKA results because of heterogeneity of study methodologies and results. Further high-quality research is required.

A systematic review of preoperative determinants of patient-reported pain and physical function up to 2 years following primary unilateral total hip arthroplasty.

UNLABELLED: Although generally considered successful, total hip arthroplasty (THA) can yield suboptimal results in terms of pain and function in up to one forth of patients suffering from hip osteoarthritis (OA). A thorough understanding of the determinants of patient-reported pain and function following THA can help plan interventions directed at improving surgical results. Previously published systematic reviews do not permit to confidently identify the determinants of THA outcomes because of unsatisfactory methodological designs. Therefore, we aimed to answer: (1) which preoperative factors are most consistently associated with postoperative patient-reported pain and function up to 2 years following primary unilateral THA for hip OA. Medline, Pubmed, Embase and CINAHL were screened from their respective inception dates until April 2015 using a combination of keywords and MESH terms. Criteria for inclusion were: (1) participants with primary unilateral THA for hip OA followed for at least 3 months with a maximal follow-up of 2 years; (2) validated disease-specific patient-reported outcome measures assessing pain and/or disability; (3) identification of determinants obtained via multivariate analyses. Methodological quality was assessed using a modified version of the methodology checklist for prognostic studies. Twenty-two manuscripts were included. Mean score of the methodological quality was 81.0±10.3% (66.7% to 100%). Among socioeconomic determinants, a lower educational level was significantly related to worse pain and function (3 out of 3 studies evaluating the relationship). Clinical determinants of poor outcomes included preoperative levels of pain and physical function (9 out of 12 studies), higher body mass index (6 out of 10 studies), presence/greater level of comorbidities (7 out of 8), worse general health (4 out of 4 studies) and lower radiographic OA severity (3 out of 4 studies). Study heterogeneity limited the pooled assessment of the strength of associations between the preoperative variables and THA outcomes. Studies with moderate-to-high methodological quality allowed to identify 6 preoperative variables consistently associated with medium term pain and function following THA. This knowledge may assist the management of patients at risk of poor results. Further research is required to clarify the force of associations between determinants and THA outcomes. LEVEL OF EVIDENCE: Level II. Systematic review of cohort studies.

Mathematical modeling of the HIV/Kaposi's sarcoma coinfection dynamics in areas of high HIV prevalence.

We formulate a deterministic system of ordinary differential equations to quantify HAART treatment levels for patients co-infected with HIV and Kaposi's Sarcoma in a high HIV prevalence setting. A qualitative stability analysis of the equilibrium states is carried out and we find that the disease-free equilibrium is globally attracting whenever the reproductive number ℛk < 1. A unique endemic equilibrium exists and is locally stable whenever ℛk > 1. Therefore, reducing ℛk to below unity should be the goal for disease eradication. Provision of HAART is shown to provide dual benefit of reducing HIV spread and the risk of acquiring another fatal disease for HIV/AIDS patients. By providing treatment to 10% of the HIV population, about 87% of the AIDS population acquire protection against coinfection with HIV and Kaposi's Sarcoma (KS). Most sub-Sahara African countries already have programmes in place to screen HIV. Our recommendation is that these programmes should be expanded to include testing for HHV-8 and KS counseling.

Optimal harvesting from a population in a stochastic crowded environment.

We study the (Ito) stochastic differential equation [equation: see text] as a model for population growth in a stochastic environment with finite carrying capacity K > 0. Here r and alpha are constants and Bt denotes Brownian motion. If r > or = 0, we show that this equation has a unique strong global solution for all x > 0 and we study some of its properties. Then we consider the following problem: What harvesting strategy maximizes the expected total discounted amount harvested (integrated over all future times)? We formulate this as a stochastic control problem. Then we show that there exists a constant optimal "harvest trigger value" x* epsilon (0, K) such that the optimal strategy is to do nothing if Xt < x* and to harvest Xt-x* if Xt > x*. This leads to an optimal population process Xt being reflected downward at x*. We find x* explicitly.