Use of Complex Lie Symmetries for Linearization of Systems of Differential Equations - II: Partial Differential Equations

The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations implies the linearizability of systems of partial differential equations corresponding to those complex ordinary differential equations. The invertible complex transformations can be used to obtain invertible real transformations that map a system of nonlinear partial differential equations into a system of linear partial differential equation. Explicit invariant criteria are given that provide procedures for writing down the solutions of the linearized equations. A few non-trivial examples are mentioned.Comment: This paper along with its first part ODE-I were combined in a single research paper "Linearizability criteria for systems of two second-order differential equations by complex methods" which has been published in Nonlinear Dynamics. Due to citations of both parts I and II these are not replaced with the above published articl

Cost of intensive care services at a central hospital in South Africa

Background. Intensive care services are one of the largest cost drivers in a hospital. Increasing life expectancy and comorbidities have resulted in an increased need for intensive care beds.Objectives. To conduct a cost analysis of intensive care services at a central hospital in the public sector in South Africa (SA).Methods. A retrospective cost analysis for the 2015/16 financial year was conducted across two intensive care units (ICUs), a trauma ICU (10 beds) and a combined ICU for neurosurgery, medicine and surgery (18 beds). A mixed-methods costing approach was used based on the availability of data. The bottom-up approach was used to calculate the cost of clinical support, pharmaceuticals, consumables and human resources. The top-down approach was used to allocate the cost of equipment and goods and services.Results. There were 544 admissions resulting in 4 987 inpatient days during the study period. The total estimated inpatient cost across the two ICUs was ZAR114 055 104, with a cost per patient day of ZAR22 870. The combined ICU cost per patient day was 58% higher than the cost per patient day in the trauma ICU (ZAR26 954 v. ZAR17 021). The mean cost per admission was ZAR157 883 in the trauma ICU and ZAR245 087 in the combined ICU. Human resources costs were the highest ICU cost driver (55%), followed by direct patient activity costs (medical consumables, pharmaceuticals, laboratory tests, radiology and blood products), which contributed 24%.Conclusions. This is the first reported cost analysis of intensive care services in SA. Our cost per patient day was higher than that reported in other lower-income countries, but lower than that in high-income countries. These costs vary owing to the different types of ICUs, wide spectrum of disease presentation and availability of diagnostic and treatment options. This study provides useful data that could assist in the planning and provision of intensive care services

Conditional linearizability criteria for a system of third-order ordinary differential equations

We provide linearizability criteria for a class of systems of third-order ordinary differential equations (ODEs) that is cubically semi-linear in the first derivative, by differentiating a system of second-order quadratically semi-linear ODEs and using the original system to replace the second derivative. The procedure developed splits into two cases, those where the coefficients are constant and those where they are variables. Both cases are discussed and examples given

COVID-19: The role of artificial intelligence in empowering the healthcare sector and enhancing social distancing measures during a pandemic

Indiscriminatory in its spread, COVID-19 has engulfed communities from all social backgrounds throughout the world. While healthcare professionals work tirelessly testing for the virus and caring for patients, they too have become casualties of the pandemic. Currently the best way to attempt to curb the spread of the virus, echoed by almost all nation leaders, is to distance ourselves from one another socially or physically. However ideal this may seem, social distancing is not always practical in densely populated lower-income countries with many citizens below the breadline. With the majority of South Africans living in poverty, communities in overcrowded households are unable to distance themselves from one another appropriately. In addition, as a nation we struggle with high HIV and tuberculosis rates, malnutrition and an already overburdened healthcare system, emphasising the extreme vulnerability of our people. These factors, coupled with the fact that many of our healthcare professionals lack the necessary personal protective equipment to prevent them from contracting the virus themselves, highlight the gravity of the damaging repercussions that we may face in the coming months, after the complete national lockdown in force at the time of writing is lifted and we move towards a partial lockdown state. Nationally, there needs to be a shift in mindset towards exploring alternative technology-based preventive measures that may empower the healthcare sector in the long term and enhance social distancing

Biobank research: Time for discussion and debate

The establishment of biobanks is gaining prominence globally. The open and evolving nature of biobanks has profound ethical, legal and social implications for individual and group autonomy, informed consent, privacy, confidentiality, secondary use of samples and data over time, return of results, data sharing, benefit sharing with communities, and premature or unplanned closure. Complexities also emerge  because of increasing international collaborations, and differing national positions. Public consultation and involvement are very necessary to the success of biobanks. Implementing national laws in an internationally consistent manner is problematic

Stem cell tourism in South Africa: The legal position

Stem cell tourism has become a common phenomenon worldwide and is increasingly affecting South Africa, as is evident from recent media reports. We examine the South African legal framework regulating stem cell therapy, focusing first on the effects of unproven stem cell treatments, and provide recommendations that may assist in strengthening the legal position

Biobank research: Time for discussion and debate

The establishment of biobanks is gaining prominence globally. The open and evolving nature of biobanks has profound ethical, legal and social implications for individual and group autonomy, informed consent, privacy, confidentiality, secondary use of samples and data over time, return of results, data sharing, benefit sharing with communities, and premature or unplanned closure. Complexities also emerge because of increasing international collaborations, and differing national positions. Public consultation and involvement are very necessary to the success of biobanks. Implementing national laws in an internationally consistent manner is problematic