Effect of quarantine and vaccination in a pandemic situation: a mathematical modelling approach

When a pandemic occurs, it can cost fatal damages to human life. Therefore, it is important to understand the dynamics of a global pandemic in order to find a way of prevention. This paper contains an empirical study regarding the dynamics of the current COVID-19 pandemic. We have formulated a dynamic model of COVID-19 pandemic by subdividing the total population into six different classes namely susceptible, asymptomatic, infected, recovered, quarantined, and vaccinated. The basic reproduction number corresponding to our model has been determined. Moreover, sensitivity analysis has been conducted to find the most important parameters which can be crucial in preventing the outbreak. Numerical simulations have been made to visualize the movement of population in different classes and specifically to see the effect of quarantine and vaccination processes. The findings from our model reveal that both vaccination and quarantine are important to curtail the spread of COVID-19 pandemic. The present study can be effective in public health sectors for minimizing the burden of any pandemic.

Uniqueness of continuous solution to $q$-Hilfer fractional hybrid integro-difference equation of variable order

In this paper, the authors introduced a novel definition based on Hilfer fractional derivative, which name $q$-Hilfer fractional derivative of variable order. And the uniqueness of solution to $q$-Hilfer fractional hybrid integro-difference equation of variable order of the form \eqref{eq:varorderfrac} with $0 < \alpha(t) < 1$, $0 \leq \beta \leq 1$, and $0 < q < 1$ is studied. Moreover, an example is provided to demonstrate the result.

Some Integral Inequalities Involving Exponential Type Convex Functions and Applications

In this present case, we focus and explore the idea of a new family of convex function namely exponentialtype m–convex functions. To support this newly introduced idea, we elaborate some of its nice algebraicproperties. Employing this, we investigate the novel version of Hermite–Hadamard type integral inequality.Furthermore, to enhance the paper, we present several new refinements of Hermite–Hadamard (H−H) inequality.Further, in the manner of this newly introduced idea, we investigate some applications of specialmeans. These new results yield us some generalizations of the prior results in the literature. We believe, themethodology investigated in this paper will further inspire intrigued researchers.

Enhancement of heat and mass transfer of a physical model using Generalized Caputo fractional derivative of variable order and modified Laplace transform method

In this paper, we use a model of non-Newtonian second grade fluid which having three partial differentialequations of momentum, heat and mass transfer with initial condition and boundary condition. Wedevelop the modified Laplace transform of this model with fractional order generalized Caputo fractional operator.We find out the solutions for temperature, concentration and velocity fields by using modified Laplacetransform and investigated the impact of the order α and ρ on temperature, concentration and velocity fieldsrespectively. From the graphical results, we have seen that both the α and ρ have reverse effect on the fluidflow properties. In consequence, it is observed that flow properties of present model can be enhanced nearthe plate for smaller and larger values of ρ. Furthermore, we have compared the present results with theexisting literature for the validation and found that they are in good agreement.

Modeling the impact of campaign program on the prevalence of anemia in children under five

Anemia, a global health problem, is increasing worldwide and affecting both developed and developingcountries. Being a blood disorder, anemia may occur in any stages of life but it is quite common in childrenunder the age of five. Globally, iron deficiency is the supreme contributor towards the onset of anemia. In thispaper, a general model based on the dynamics of anemia among children under five is formulated. The populationis divided in three classes such as susceptible, affected and treated. A time-dependent control measurenamely campaign program is considered. The model has an equilibrium point and the stability of the pointis analyzed. Moreover, sensitivity of the equilibrium point is also performed to discover the critical parameters.Numerical simulations are carried out to observe the dynamic behavior of the model. Results showthat campaign program is effective in minimizing the disease progression. The number of child patients andyearly deaths significantly decrease with accelerated campaign program that is implemented earlier whereastermination of the applied measure may upturn the burden. Findings also reveal that application of controlmeasure helps to reduce the prevalence of anemia but may not eliminate the disease.

Uniqueness and Stability Results on Non-local Stochastic Random Impulsive Integro-Differential Equations

The paper is concerned with stochastic random impulsive integro-differential equations with non-local conditions. The sufficient conditions guarantees uniqueness of mild solution derived using Banach fixed point theorem. Stability of the solution is derived by incorporating Banach fixed point theorem with certain inequality techniques.

Computation of approximate solution to COVID-19 mathematical model

In this work, we investigate a modified population model of non-infected and infected (SI) compartmentsto predict the spread of the infectious disease COVID-19 in Pakistan. For Approximate solution, we use LaplaceAdomian Decomposition Method (LADM). With the help of the said technique, we develop an algorithmto compute series type solution to the proposed problem. We compute few terms approximate solutionscorresponding to different compartment. With the help of MATLAB, we also plot our approximate solutionsfor different compartment graphically.

Some fixed point results of F-Contraction mapping in D-metric spaces by Samet’s method

The aim of this paper is to study the F-contraction mapping introduced by Wardowski to obtain fixed point results by method of Samet in generalized complete metric spaces. Our findings extend the results announced by Samet methods and some other works in generalized metric spaces.

On Fuzzy Henstock-Kurzweil-Stieltjes-♦-Double Integral on Time scales

We introduce and study some properties of fuzzy Henstock-Kurzweil-Stietljes-$ \Diamond $-double integral on time scales. Also, we state and prove the uniform convergence theorem, monotone convergence theorem and dominated convergence theorem for the fuzzy Henstock-Kurzweil Stieltjes-$\Diamond$-double integrable functions on time scales.

On B- Covariant Derivative of First Order for Some Tensors in different Spaces

In this paper, we study the relationship between Cartan's second curvature tensor $P_{jkh}^{i}$ and $(h) hv-$torsion tensor $C_{jk}^{i}$ in sense of Berwald. Moreover, we discuss the necessary and sufficient condition for some tensors which satisfy a recurrence property in $BC$-$RF_{n}$, $P2$-Like-$BC$-$RF_{n}$, $P^{\ast }$-$BC$-$RF_{n}$ and $P$-reducible-$BC-RF_{n}$.