Role of media and treatment on an SIR model

n this paper, the impact of awareness programs as well as treatment on an SIR model has been investigated. We assume that the whole population is divided into four compartments, named as susceptible (S), infected (I), aware susceptible (Sa) and recovered (R). Analytical findings and numerical simulations of the model show that if the exposure to the awareness program is high and adequate treatment is available, then the infection can be eliminated. Analysis of the model also depicts that if treatment is not available, then infection is high even if enough awareness is present. But in absence of awareness an infection can not be eliminated inspite of adequate treatment. Effective treatment can led to a diminished level of infection. Stability analysis of the model is investigated by using stability theory of differential equations. Further, numerical simulations are carried out to validate the analytical results

Modeling the dynamics of viral–host interaction during treatment of productively infected cells and free virus involving total immune response

Virus dynamics models are useful in interpreting and predicting the change in viral load over the time and the effect of treatment in emerging viral infections like HIV/AIDS, hepatitis B virus (HBV).We propose a mathematical model involving the role of total immune response (innate, CTL, and humoral) and treatment for productively infected cells and free virus to understand the dynamics of virus–host interactions. A threshold condition for the extinction or persistence of infection, i.e. basic reproductive number, in the presence of immune response (RI ) is established. We study the global stability of virus-free equilibrium and interior equilibrium using LaSalle’s principle and Lyapunov’s direct method. The global stability of virus-free equilibrium ensures the clearance of virus from the body, which is independent of initial status of subpopulations. Central manifold theory is used to study the behavior of equilibrium points at RI = 1, i.e. when the basic reproductive number in the presence of immune response is one. A special case, when the immune response (IR) is not present, has also been discussed. Analysis of special case suggests that the basic reproductive number in the absence of immune response R0 is greater than that of in the presence of immune response RI , i.e. R0> RI . It indicates that infection may be eradicated if RI  < 1. Numerical simulations are performed to illustrate the analytical results using MatLab and Mathematica

Dynamics of an SIR Model with Nonlinear Incidence and Treatment Rate

In this paper, global dynamics of an SIR model are investigated in which the incidence rate is being considered as Beddington-DeAngelis type and the treatment rate as Holling type II (saturated). Analytical study of the model shows that the model has two equilibrium points (diseasefree equilibrium (DFE) and endemic equilibrium (EE)). The disease-free equilibrium (DFE) is locally asymptotically stable when reproduction number is less than one. Some conditions on the model parameters are obtained to show the existence as well as nonexistence of limit cycle. Some sufficient conditions for global stability of the endemic equilibrium using Lyapunov function are obtained. The existence of Hopf bifurcation of model is investigated by using Andronov-Hopf bifurcation theorem. Further, numerical simulations are done to exemplify the analytical studies

On the categories of L-Valued and Q-Valued 6 deterministic fuzzy automata

Automata and languages have been studied in the context of different lattice structures by several authors. This paper is toward the categorical study of deterministic lattice-valued (L-valued) fuzzy automata and deterministic quantale-valued (Q-valued) fuzzy automata. The existence of initial and final objects in the subcategory of category of deterministic lattice-valued fuzzy automata is shown. We also show that there is an adjunction between the category of deterministic lattice-valued and quantale-valued fuzzy automata

Anticancer efficacy of phenolics based structurally related compounds and their radical scavenging action

Cancer, one of the leading causes of death worldwide, is an abnormal cell proliferation that fails to respond to the normal signals. In an effort to eradicate the growing menace of cancer, a clear understanding of fundamental biology and molecular mechanism of carcinogenesis is essential for targeted therapies. Among the devised strategies in use for cancer treatment, the one that is of immense interest is the development of plant based novel anticancer agents. Due to their tremendous availability, biological activity and efficacy, the phytochemicals deemed a gibbous future in chemoprevention. In the present study, several phenolics based structurally related compounds of steroidal and non-steroidal skeleton were synthesized and tested for their modulatory effect on ornithine decarboxylase activity, an enzyme highly upregulated in cancer. Additionally, these compounds were also examined for radical scavenging extent to establish a correlation with the anticancer property. Our result suggests that the tested compounds possessed radical scavenging activity, for being the inherent property of the phenolics. 3-(3’,4’5’-trimethoxyphenyl)-4,5,6-trimethoxyindan-1-one oxime exhibited highest inhibition of enzyme activity (91%) followed by 1-(2,4-dibromophenyl)-3-[3-methoxyestra 1,3,5(10)-trien-17-acetate,2-yl]-2-propen-1-one (85%), 2-Hydroxy, 3-(3’,4’,5’-trimethoxy phenyl)-4,5,6-trimethoxy ind-2-en-1-one (80%), 1-(3,4-methylenedioxyphenyl)-3-(3,4,5-trimethoxyphenyl)-2-propen-1-one (74%) and 1-(3,-methoxy, 4-hydroxyphenyl)-3-[3-methoxyestra 1,3,5(10)-trien-17-acetate, 2-yl]-2-propen-1-one (67%). Furthermore, it was observed that 1-(3-Methoxy, 4- hydroxyphenyl)-3-[3-methoxyestra 1,3,5 (10)-trien-17-acetate, 2-yl]-2-propen-1-one showed the highest scavenging effect (67%) in nitric oxide assay, whereas 1-(3-methylphenyl)-3-[3-methoxy, 17-hydroxyestra 1,3,5(10)-trien, 2-yl]-2-propen-1-one showed maximum inhibition of radical formation in 2,2-diphenyl-1-picrylhydrazyl analysis. Most of these compounds possessed a 3,4,5-trimethoxyphenyl unit which might be inducing enzyme inhibition and scavenging radical formation. Further investigations are on the way to establish the structure-activity relationship, so that these compounds can be developed as anticancer agents

An extinct vertebrate preserved by its living hybridogenetic descendant.

Hybridogenesis is a special mode of hybrid reproduction where one parental genome is eliminated and the other is transmitted clonally. We propose that this mechanism can perpetuate the genome of extinct species, based on new genetic data from Pelophylax water frogs. We characterized the genetic makeup of Italian hybridogenetic hybrids (P. kl. hispanicus and esculentus) and identified a new endemic lineage of Eastern-Mediterranean origin as one parental ancestor of P. kl. hispanicus. This taxon is nowadays extinct in the wild but its germline subsists through its hybridogenetic descendant, which can thus be considered as a "semi living fossil". Such rare situation calls for realistic efforts of de-extinction through selective breeding without genetic engineering, and fuels the topical controversy of reviving long extinct species. "Ghost" species hidden by taxa of hybrid origin may be more frequent than suspected in vertebrate groups that experienced a strong history of hybridization and semi-sexual reproduction

Compensation of atmospheric CO2 buildup through engineered chemical shrinkage

Retrieval of background carbon dioxide into regional chemical extractors would counter anthropogenic inputs in a manner friendly to established industries. We demonstrate via atmospheric transport/scaling calculations that for idealized flat removal units, global coverage could be less than two hundred thousand square kilometers. The disrupted area drops to a small fraction of this with engineering into the vertical to bypass laminarity. Fence structures and artificial roughness elements can both be conceived. Sink thermodynamics are analyzed by taking calcium hydroxide as a sample reactant. Energy costs could be minimized at near the endothermicity of binding reversal. In the calcium case the value is 25 kcal mole-1, as against a fuel carbon content of 150 in the same units. Aqueous kinetics are less than favorable for the hydroxide, but misting could counteract slow liquid phase transfer. Properties of superior scrubbers are outlined