Solution of an SEIR Epidemic Model in Fractional Order

In this paper, we consider the SEIR (Susceptible-Exposed-Infected-Recovered) epidemic model (with out of bilinear incidence rates) in fractional order. First the non-negative solution of the SEIR model in fractional order is discussed. Then calculate an approximate solution of the proposed model. The obtained results are compaired with those obtained by forth order Runge-Kutta method and nonstandard numerical method in the integer case. Finally, we present some numerical results

Control of COVID-19 dynamics through a fractional-order model

We investigate, through a fractional mathematical model, the effects of physical distance on the SARS-CoV-2 virus transmission. Two controls are considered in our model for eradication of the spread of COVID-19: media education, through campaigns explaining the importance of social distancing, use of face masks, etc., towards all population, while the second one is quarantine social isolation of the exposed individuals. A general fractional order optimal control problem, and associated optimality conditions of Pontryagin type, are discussed, with the goal to minimize the number of susceptible and infected while maximizing the number of recovered. The extremals are then numerically obtained.publishe

Identification and Analysis of Factors Affecting Machinery in the Construction Industry of Pakistan

This research has been carried out to explore the current practices of machinery used in the construction industry of building projects of Pakistan. Management of construction equipment varies from project to project and organization. Small to medium contractors normally purchase used equipment required for their projects, because smaller equipment can be purchased and managed more easily. On the other hand, larger contractors often subcontract equipment/ machines to perform the specific tasks of the project. This research work revealed different factors of machinery management. Factors causing cost overrun in the construction projects were ranked on the basis of Relative Importance Index (RII). Top five significant factors identified were frequent equipment breakdowns, maintenance of equipment, insufficient number of equipment, performance / efficiency of equipment and inadequate modern equipment

Fuzzy Analysis of Artificial Drug Transmission Model with Optimal Control

This article presents an artificial drug abusers system consolidating the impact of treatment with psychological and physiological addicts under fuzzy parameters. In the fuzzy model, all of the parameters are considered to be triangular fuzzy numbers to represent the uncertainty that pervaded the dynamics. To handle the arrangements while avoiding problems, the fuzzy model is turned into a defuzzified model using the utility function method. The fuzzy model’s positivity and boundedness are carefully explored, and an equilibrium analysis is also completed. Both the drug-addict equilibrium and the drug-free equilibrium have established stability analyses. This article explains fuzzy optimum control using Pontryagin’s maximum principle. Finally, it is shown that the treatment alongside counselling and conducting awareness programs is more fruitful and drug-related controlling is more viable in the fuzzy nature. Likewise, we plot the 3D associations with fuzzy parameters which show the inventiveness and appropriateness of the results.2022-2

A general chemostat model with second-order Poisson jumps: asymptotic properties and application to industrial waste-water treatment

A chemostat is a laboratory device (of the bioreactor type) in which organisms (bacteria, phytoplankton) develop in a controlled manner. This paper studies the asymptotic properties of a chemostat model with generalized interference function and Poisson noise. Due to the complexity of abrupt and erratic fluctuations, we consider the effect of the second order Itô-Lévy processes. The dynamics of our perturbed system are determined by the value of the threshold parameter $\mathfrak{C}^{\star}_0$. If $\mathfrak {C}^{\star}_0$ is strictly positive, the stationarity and ergodicity properties of our model are verified (practical scenario). If $\mathfrak {C}^{\star}_0$ is strictly negative, the considered and modeled microorganism will disappear in an exponential manner. This research provides a comprehensive overview of the chemostat interaction under general assumptions that can be applied to various models in biology and ecology. In order to verify the reliability of our results, we probe the case of industrial waste-water treatment. It is concluded that higher order jumps possess a negative influence on the long-term behavior of microorganisms in the sense that they lead to complete extinction

Investigation of anti-nociceptive, anti-inflammatory potential and ADMET studies of pure compounds isolated from Isodon rugosus Wall. ex Benth

The strong ethnopharmacological utilization of Isodon rugosus Wall. Ex. Benth is evident in the treatment of several types of pain and inflammation, including toothache, earache, abdominal pain, gastric pain, and generalized body pain and inflammation. Based on this background, the antinociceptive effects of the crude extract, various fractions, and essential oil have been reported previously. In this research work, we isolate and characterize pure bioactive compounds from I. rugosus and evaluate possible mechanisms using various in vivo and in vitro models. The pure compounds were analyzed for analgesic and anti-inflammatory activities through various assays. The column chromatography of the chloroform fraction of I. rugosus led to the identification of two pure compounds, i.e., 1 and 2. Compound 1 demonstrated notable inhibition (62% writhing inhibition, 72.77% COX-2 inhibition, and 76.97% 5-LOX inhibition) and anti-inflammatory potential (>50% paw edema inhibition at various intervals). The possible mechanism involved in antinociception was considered primarily, a concept that has already been elucidated through the application of naloxone (an antagonist of opioid receptors). The involvement of adrenergic receptors was investigated using a hot plate model (an adrenergic receptor antagonist). The strong ethnomedicinal analgesic background of I. rugosus, supported by previous reports and current observations, leads to the conclusion that I. rugosus is a potential source of antinociceptive and anti-inflammatory bioactive compounds. It may be concluded from the results that the isolated analgesic compounds of I. rugosus may be a possible alternative remedy for pain and inflammation management with admirable efficacy and safety profiles

Letter to the Editor Comment on (Transmission Model of Hepatitis B Virus with Migration Effect)

We show the erroneous assumptions and reasoning by introducing the migration effect of individuals in the transmission model of Hepatitis B virus. First, some false results related to the eigenvalues and reproductive number in the recent literature in mathematical biology will be presented. Then, it will be proved that the product of the matrices in the next generation method to obtain the reproductive number 0 is not correct and the local and global stability results based on the reproductive number 0 are considered false. Model Formulation In this section, we consider the model developed by Khan et al. (i) the transmission rate 1 from migrated class to exposed class, (ii) the transmission rate 2 from migrated to acute class, (iii) the death rate of the migrated class. The model presented in [1] is given by They have claimed that the migrated class of individuals come from different parts of the world to the host country, and their interaction occurs in the form of sexual interactions, blood transportation, and transfusion. What are the parameters in the model that bring out the migrated class? The authors hav