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During the past two years, the novel coronavirus pandemic has dramatically affected the world by producing 4.8 million deaths. Mathematical modeling is one of the useful mathematical tools which has been used frequently to investigate the dynamics of various infectious diseases. It has been observed that the nature of the novel disease of coronavirus transmission differs everywhere, implying that it is not deterministic while having stochastic nature. In this paper, a stochastic mathematical model has been investigated to study the transmission dynamics of novel coronavirus disease under the effect of fluctuated disease propagation and vaccination because effective vaccination programs and interaction of humans play a significant role in every infectious disease prevention. We develop the epidemic problem by taking into account the extended version of the susceptible-infected-recovered model and with the aid of a stochastic differential equation. We then study the fundamental axioms for existence and uniqueness to show that the problem is mathematically and biologically feasible. The extinction of novel coronavirus and persistency are examined, and sufficient conditions resulted from our investigation. In the end, some graphical representations support the analytical findings and present the effect of vaccination and fluctuated environmental variation. [ABSTRACT FROM AUTHOR]

This study was carried out to find the environmental factors which have a significant effect on the productive and reproductive characteristics of the Balochi sheep. The study used data from 729 ewes and 71 rams for a period of 13 years (2003 to 2016) at the Sheep Research Center, Yet Abad, Balochistan, Pakistan. The productive characteristics considered for current study were weight, birth weight (BW), 90 days weight (3 MW), 180 days weight (6 MW), 270 days weight (9 MW), 365 days (12 MW), and 2 years weight (24 MW). Reproductive characteristics measured were ewe age at first service (AFS), service period (SP) of ewe, age at 1st lambing (AFL) of ewe, lambing interval (LI), and sex ratio. Restricted maximum likelihood (REML) assessments of different characteristics were analyzed for the Balochi sheep on the basis of location, birth year (YOB), season of birth (SOB), type of birth (TOB), and sex of lamb. The average means ± SE for BW, WW, 6 MW, 9 MW, 12 MW, and 24 MW, were 3.28 ± 0.83, 17.20 ± 2.04, 21.94 ± 1.60, 26.20 ± 2.87, 30.21 ± 3.58, and 37.11 ± 2.84 for ram and 2.56 ± 0.53, 15.69 ± 1.45, 19.57 ± 1.77, 24.07 ± 2.70, 27.46 ± 2.09, and 34.61 ± 2.32 for ewes respectively. The results of reproductive performance of the Balochi sheep age of ewe at the time of breeding, age at first service (AFS), service period (SP), age at first lambing (AFL), and lambing interval (LI) were 1078 ± 2.2, 579.61 ± 0.6, 206.25 ± 0.2, 731.67 ± 0.3, and 256.60 ± 0.3 days respectively. The twining and lambing rates were 10.12% and 86.78%, while the sex proportion for ram and ewes was 50.12:49.37. Area, sex, and TOB had a significant (p < 0.05) effect on weight while TOB (twinning rate) was higher in Balochi sheep. These conditions affected the productive and reproductive performance of the Balochi sheep. At Sheep Research Center, Yet Abad, Balochistan, Pakistan, performed fundamentally better in all qualities such as weight gain and reproductive performance. Supplements were given with feed to get maximum profit from the sheep of Yet Abad farm. The birth weight of males was higher than that of females and single conceived Balochi sheep were heavier than that of twins. Thus, it was concluded that the Balochi sheep can be improved with better management practices, feeding, and disease control. [ABSTRACT FROM AUTHOR]

In this article, we extend the notion of double Laplace transformation to triple and fourth order. We first develop theory for the extended Laplace transformations and then exploit it for analytical solution of fractional order partial differential equations (FOPDEs) in three dimensions. The fractional derivatives have been taken in the Caputo sense. As a particular example, we consider a fractional order three dimensional homogeneous heat equation and apply the extended notion for its analytical solution. We then perform numerical simulations to support and verify our analytical calculations. We use Fox-function theory to present the derived solution in compact form. [ABSTRACT FROM AUTHOR]

In tropical countries, one of the major threats for diary animal production is climate change. Ambient management interventions are beneficial and are the dire need of animal production in tropics. Ambient management intervention and its effect on physiological performance of lactating NiliRavi buffaloes were investigated during the hot dry months (April to June) of Pakistan. Fifteen lactating NiliRavi water buffaloes of similar size, age, and same parity were randomly stratified into three groups, comprising of five animals in each group, designated as group S, SF, and SFS. Animals of group S (control) were kept just under the shade while the animals in group SF were provided shade plus fan, animals in group SFS were provided the shade, fan as well as sprinklers during the hot day hours between 10:00 AM to 6:00 PM. Shed conditions were same for all animals, isonitrogenous and isocaloric feed was provided to all animals. Milk production decreased with the increase in ambient temperature. Average dry matter intake in group S, SF, and SFS were 75%, 80%, and 90% of the total feed offered to the experimental animals, respectively. The mean rectal temperatures (°F) were 101.69, 101.19, and 100.85 in group S, SF, and SFS, respectively. Heat stress had pronounced effect on blood glucose level as indicated by the mean glucose concentration in group S and SFS being recorded at 78.04 mg/dl and 90.47 mg/dl, respectively. It is concluded that the buffaloes should be provided with sprinklers and fans to minimize heat load and maximize the production during hot dry season. [ABSTRACT FROM AUTHOR]

This investigation aims at studying a Euler-Maruyama (EM) approximate solutions scheme for stochastic differential equations (SDEs) in the framework of G-Brownian motion. Subject to the growth condition, it is shown that the EM solutions $ Z^q(t)$ are bounded, in particular, $ Z^q(t)\in M_G^2([t_0,T];\mathbb{R}^n)$ . Letting Z( t) as a unique solution to SDEs in the G-framework and utilizing the growth and Lipschitz conditions, the convergence of $ Z^q(t)$ to Z( t) is revealed. The Burkholder-Davis-Gundy (BDG) inequalities, Hölder's inequality, Gronwall's inequality and Doobs martingale's inequality are used to derive the results. In addition, without assuming a solution of the stated SDE, we have shown that the Euler-Maruyama approximation sequence $ \{Z^q(t)\}$ is Cauchy in $ M_G^2([t_0,T];\mathbb{R}^n)$ thus converges to a limit which is a unique solution to SDE in the G-framework. [ABSTRACT FROM AUTHOR]

The ancient grain is becoming enormously popular in modern food regimen in many countries; the higher proportion of α-linolenic acid makes chia the superb source of omega-3 fatty (about 65 % of the oil content). Omega-3 fatty acid has been associated with a large number of physiological functions in human body. Chia seed is a potential source of antioxidants with the presence of chlorogenic acid, caffeic acid, myricetin, quercetin, and kaempferol which are believed to have cardiac, hepatic protective effects, anti-ageing and anti-carcinogenic characteristics. It is also a great source of dietary fibre which is beneficial for the digestive system and controlling diabetes mellitus with higher concentration of beneficial unsaturated fatty acids, gluten free protein, vitamin, minerals and phenolic compounds. Therapeutic effects of chia in the control of diabetes, dyslipidaemia, hypertension, as anti-inflammatory, antioxidant, anti-blood clotting, laxative, antidepressant, antianxiety, analgesic, vision and immune improver is scientifically established. [ABSTRACT FROM AUTHOR]

Omega 3 and 6 fatty acids were enriched in the olein fraction of chia oil via dry fractionation at −30°C. Concentrations of C18:3 (linolenic acid, ω-3) and C18:2 (linoleic acid, ω-6) were 78.16 and 25.42% in the olein fraction. HPLC characterization indicated enrichment of caffeic and chlorogenic acids, quercetin, and phenolic glycosides in the olein fraction. Total antioxidant activities of chia oil and the olein and stearin fractions were 42.5, 53.8, and 34.6%, respectively. After 6 months of storage at 4°C, the concentration of ω-3 in the olein fraction decreased from 78.19 to 76.16%, with a 10% decrease in the ω-3 concentration when the olein fraction was stored at 25°C. The stearin fraction of chia oil exhibited the longest induction period, followed by chia oil and the olein fraction. Amounts of ω-3 and 6 fatty acids can be enriched in the olein fraction from 11.92 and 61.28% to 15.22 and 72.16%, respectively, with reasonable storage stability at low temperature. [ABSTRACT FROM AUTHOR]

Antioxidant characteristics of ice cream supplemented with sugarcane juice were investigated. An original 13% sucrose content in ice cream was supplemented with 20, 40, and 60% sugarcane juice (82, 164, and 246 mL/L, treatments T, T, and T, respectively). The sucrose content of all treatments was 13%. DPPH free radical scavenging activities of control, T, T, and T ice cream samples were 5.64±0.19, 16.39±0.15, 37.66±1.21, and 55.78±0.98%, respectively, with total flavonoid contents of 0.18±0.02, 0.51±0.04, 0.92±0.09, and 1.65±0.14 mg of quercetin equivalents/mL, respectively. The nitric oxide free radical scavenging activities were 2.36±0.17, 7.12±0.32, 18.67±0.55, and 42.35±2.36%, respectively. Addition of sugarcane juice to ice cream inhibited oxidation of unsaturated fatty acids during storage for 180 days with no effect on sensory characteristics for the T and T treatment levels. Sugarcane juice can be used in formulation of ice cream to enhance concentrations of natural antioxidants. [ABSTRACT FROM AUTHOR]