A simple mathematical model for the spread of two political parties

In this paper, a non-linear mathematical model for the spread of two political parties has been proposed and analyzed by using epidemiological approach. The whole population is assumed to be a constant and homogeneously mixed. Equilibria have been obtained analytically and their local and global stability have been discussed. Conditions for the co-existence of both the political parties have been obtained. Numerical simulation is also performed to support the analytical results

Modeling the impact of mitigation options on abatement of methane emission from livestock

Mitigation of methane emission from livestock sector is crucial to combat the menace of global warming. In the present paper, a nonlinear mathematical model is proposed to investigate the impact of mitigation options, for curtailing livestock methane emission, on the reduction of atmospheric concentration of methane. In modeling process, it is assumed that the mitigation options are applied at a rate proportion to the livestock population. The conditions for reduction and stabilization of atmospheric methane have been obtained. Numerical simulation has been performed to verify the analytical findings by taking the secondary data of atmospheric concentration of methane, human and livestock populations. Sensitivity analysis is carried out to explore the impact of the key parameters of the model system

Combating unemployment through skill development

In this paper, we propose and analyze a nonlinear mathematical model to study the effect of skill development on unemployment. We assume that government promulgates different levels of skill development programs for unemployed persons through which two different categories of skilled persons, namely, the low-skilled and the highly-skilled persons, are coming out and the highly-skilled persons are able to create vacancies. The model is studied using stability theory of nonlinear differential equations. We find analytically that there exists a unique positive equilibrium point of the proposed model system under some conditions. Also, the resulting equilibrium is locally as well as globally stable under certain conditions. The effective use of implemented policies to control unemployment by providing skills to unemployed persons and the new vacancies created by highly-skilled persons are identified by using optimal control analysis. Finally, numerical simulation is carried out to support analytical findings

Modeling the effect of economic efforts to control population pressure and conserve forestry resources

The increase in human population poses a great menace for the forestry resources. Therefore, protection and conservation of forestry resources is a challenging subject across the globe. Keeping this point in view, we propose and analyze a nonlinear mathematical model to assess the effect of economic efforts applied to control population pressure as well as to increase forestry resources by plantation on the conservation of forestry resources. The condition when one should spend more money on plantation/reducing population pressure has been obtained. Numerical simulation is also performed to support analytical findings and identify the important parameters useful for the conservation of forestry resources

Charmonium production in hot magnetized hyperonic matter -- effects of baryonic Dirac sea and PV mixing

We investigate the medium modifications of the masses of pseudoscalar open charm ($D$ and $\bar D$) mesons and the charmonium state ($\psi(3770)$) in magnetized hot isospin asymmetric strange hadronic medium within a chiral effective model. The partial decay widths of $\psi(3770)$ to $D\bar D$ mesons are computed from the medium modifications of the in-medium masses of these mesons, using (I) the $^3P_0$ model and (II) a field theoretical (FT) model of composite hadrons with quark (and antiquark) constituents. The production cross-sections of $\psi(3770)$, arising from scattering of the $D$ and $\bar D$ mesons are obtained from the in-medium masses and the decay widths of the charmonium state. The effects of the magnetic field are considered due to the Dirac sea (DS) of the baryons, the mixing of the pseudoscalar ($S$=0) and vector ($S$=1) meson (PV mixing), the Landau level contributions for the charged hadrons. The anomalous magnetic moments (AMMs) of the baryons are also taken into account in the present study. For $\rho_B=\rho_0$, the inclusion of hyperons in the medium is observed to lead to magnetic catalysis (MC), contrary to inverse magnetic catalysis (IMC) observed for magnetized nuclear matter. The production cross-section of $\psi(3770)$ in the hot magnetized strange hadronic matter is observed to have a distinct double peak structure arising from the PV mixing. This is because of the fact that the mass of the longitudinal component of the charmonium state is modified by PV mixing, whereas, the masses of the transverse components remain unaffected. These can have observable consequences on the dilepton spectra as well as on the production of the charm mesons in ultra-relativistic peripheral heavy ion collision experiments, where the produced magnetic field is huge.Comment: 43 pages, 13 figures, major revisio

Modeling the effect of deforestation caused by human population pressure on wildlife species

The increase in human population has posed several problems for the ecosystem. One of these problems is the decrease in forestry resources, which leads to decline in forest area and thus threaten the survival of wildlife species as the intraspecific competition among the wildlife species increases. Moreover, these wildlife species can also be apprehended easily by poachers and smugglers. This affects the biodiversity across the globe. In this paper, we have proposed and analyzed a nonlinear mathematical model to see the effect of deforestation caused by population and its pressure on wildlife species. The analysis of proposed model reveals that, as the parameters in respect to the increase in population pressure increase, wildlife species decrease. To support analytical findings, we have done numerical simulation

Differentially localized survivin and STAT3 as markers of gastric cancer progression: Association with Helicobacter pylori

BackgroundLocalization and differential expression of STAT3 and survivin in cancer cells are often related to distinct cellular functions. The involvement of survivin and STAT3 in gastric cancer has been reported in separate studies but without clear understanding of their kinetics in cancer progression.MethodsWe examined intracellular distribution of STAT3 and survivin in gastric adenocarcinoma and compared it with normal and precancer tissues using immunoblotting and immunohistochemistry.ResultsAnalysis of a total of 156 gastric samples comprising 61 histologically normal, 30 precancerous tissues (comprising intestinal metaplasia and dysplasia), and 65 adenocarcinomas, collected as endoscopic biopsies from treatment naïve study participants, revealed a significant (P < .001) increase in overall protein levels. Survivin expression was detectable in both cytoplasmic (90.8%) and nuclear (87.7%) compartments in gastric adenocarcinomas lesions. Precancerous dysplastic gastric lesions exhibited a moderate survivin expression (56.7%) localized in cytoplasmic compartment. Similarly, STAT3 and pSTAT3 expression was detected at high level in gastric cancer lesions. The levels of compartmentalized expression of survivin and STAT3/pSTAT3 correlated in precancerous and adenocarcinoma lesions. Although overexpression of these proteins was found associated with the tobacco use and alcohol consumption, their expression invariably and strongly correlated with concurrent Helicobacter pylori infection. Receiver operating characteristic analysis of nuclear survivin, STAT3, and pSTAT3 in different study groups showed acceptable positive and negative predictive values with area under the curve above 0.8 (P < .001).ConclusionOverall, our results suggest that overall increase in survivin and STAT3 and their subcellular localization are key determinants of gastric cancer progression, which can be collectively used as potential disease biomarkers and therapeutic targets for gastric cancer.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/144680/1/cnr21004-Supplementary_Methods_20180313.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/144680/2/cnr21004-sup-0001-F1.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/144680/3/cnr21004_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/144680/4/cnr21004.pd

Evaluation of antioxidative, analgesic and anti-inflammatory activities of methanolic extract of Myrica nagi leaves : an animal model approach

Myrica nagi (family Myricaceae) is commonly known as Kathphal (Hindi) and Bayberry (English) and it has a long history of usage in traditional medicine. It is popular actinorhizal plant for its symbiotic relationship with Frankia. This study was taken in force to estimate the analgesic, anti-inflammatory and anti-oxidative activities of methanolic extract of Myrica nagi (MMN) in an animal model. Anti-oxidative property of MMN was assessed by free radical scavenging assay (DPPH method). The acute toxicity test of methanolic extract of MMN revealed that the median lethal dose (LD50) was found to be 2080 mg/kg body weight in mice. The anti-inflammatory property was evaluated by carrageenan-induced acute inflammation in rats by measuring rat paw volume at different time intervals and toxicological analysis using mice. The analgesic effect was measured in Wistar rats using the acetic acid-induced writhing test and MMN at 200 mg/kg BW showed 54.56 % inhibition of writhing. MMN showed higher anti-oxidant activity in DPPH assays as compared to standard. High dose of MMN showed a significant reduction (21.71 %) in inflammation after 4 h of treatment, which was comparable to diclofenac (10 mg/kg BW; 32.75 %)-treated group. Significant reduction (p < 0.05) in the levels of inflammatory cytokine (IL-1 beta and TNF-alpha) markers were also observed in serum of MMN-treated animals as compared to control. Taken together, the phenolic compounds of MMN may serve as potential herbal drug for amelioration of acute inflammation due to their modulatory action on free radicals

Fear effect in a three-species food chain model with generalist predator

Within the framework of a food web, the foraging behavior of meso-carnivorous species is influenced by fear responses elicited by higher trophic level species, consequently diminishing the fecundity of these species. In this study, we investigate a three-species food chain model comprising of prey, an intermediate predator, and a top predator. We assume that both the birth rate and intraspecies competition of prey are impacted by fear induced by the intermediate predator. Additionally, the foraging behavior of the intermediate predator is constrained due to the presence of the top predator. It is essential to note that the top predators exhibit a generalist feeding behavior, encompassing food sources beyond the intermediate predators. The study systematically determines all feasible equilibria of the proposed model and conducts a comprehensive stability analysis of these equilibria. The investigation reveals that the system undergoes Hopf bifurcation concerning various model parameters. Notably, when other food sources significantly contribute to the growth of the top predators, the system exhibits stable behavior around the interior equilibrium. Our findings indicate that the dynamic influence of fear plays a robust role in stabilizing the system. Furthermore, a cascading effect within the system, stemming from the fear instigated by top predators, is observed and analyzed. Overall, this research sheds light on the intricate dynamics of fear-induced responses in shaping the stability and behavior of multi-species food web systems, highlighting the profound cascading effects triggered by fear mechanisms in the ecosystem