Mathematical modeling and dynamics of immunological exhaustion caused by measles transmissibility interaction with HIV host.

This paper mainly addressed the study of the transmission dynamics of infectious diseases and analysed the effect of two different types of viruses simultaneously that cause immunodeficiency in the host. The two infectious diseases that often spread in the populace are HIV and measles. The interaction between measles and HIV can cause severe illness and even fatal patient cases. The effects of the measles virus on the host with HIV infection are studied using a mathematical model and their dynamics. Analysing the dynamics of infectious diseases in communities requires the use of mathematical models. Decisions about public health policy are influenced by mathematical modeling, which sheds light on the efficacy of various control measures, immunization plans, and interventions. We build a mathematical model for disease spread through vertical and horizontal human population transmission, including six coupled nonlinear differential equations with logistic growth. The fundamental reproduction number is examined, which serves as a cutoff point for determining the degree to which a disease will persist or die. We look at the various disease equilibrium points and investigate the regional stability of the disease-free and endemic equilibrium points in the feasible region of the epidemic model. Concurrently, the global stability of the equilibrium points is investigated using the Lyapunov functional approach. Finally, the Runge-Kutta method is utilised for numerical simulation, and graphic illustrations are used to evaluate the impact of different factors on the spread of the illness. Critical factors that effect the dynamics of disease transmission and greatly affect the rate and range of the disease's spread in the population have been determined through a thorough analysis. These factors are crucial in determining the expansion of the disease.

Different variants of pandemic and prevention strategies: A prioritizing framework in fuzzy environment.

In this trying time for the world battling different variants of the COVID'19 pandemic, different intervention strategies are being taken by government, to limit the spread of infection. Closing educational institutes, stay at home orders, campaigns for emphasis on vaccination, usage of medical mask and frequently sanitizing hands, etc. are the endeavors made by the authorities to decrease the number of cases in the country. In this regard, the contribution aims to help the decision-makers to identify a potential prevention strategy, based on public acceptance and intervention effectiveness. To achieve this objective, feasible judgments of professionals from three different sectors are brought together through meetings. Opinions, based on ten criteria, are recorded in linguistic form for prioritizing six alternatives. The linguistic terms are then evaluated and manipulated by entailing triangular fuzzy numbers and a group multi-criteria decision making (GMCDM) approach. After using the fuzzy analytical hierarchy process (F-AHP) for the complex decisions, the fuzzy VIsekriterijumsko KOmpromisno Rangiranje method (F-VIKOR) is utilized to attain the closest ideal stratagem. Consequently, through the ranking orders of defuzzified scores, intuitive preference of compromise solutions is suggested. The tactic gaining more priority with respect to the group utility to the majority and F-VIKOR index is complete lockdown for the short term. Furthermore, a comparison analysis is also added in the discussion to verify the attained prioritized outcomes. This comparative study is carried out through the technique for order of preference by similarity to ideal solution (TOPSIS), which evidently produces the same preference of alternatives. In addition, this strategy can be apparently discovered to be an effective strategy adopted by different countries in successfully decreasing the number of cases.

Optimal surveillance mitigation of COVID'19 disease outbreak: Fractional order optimal control of compartment model.

In present time, the whole world is in the phase of war against the deadly pandemic COVID'19 and working on different interventions in this regard. Variety of strategies are taken into account from ground level to the state to reduce the transmission rate. For this purpose, the epidemiologists are also augmenting their contribution in structuring such models that could depict a scheme to diminish the basic reproduction number. These tactics also include the awareness campaigns initiated by the stakeholders through digital, print media and etc. Analyzing the cost and profit effectiveness of these tactics, we design an optimal control dynamical model to study the proficiency of each strategy in reducing the virulence of COVID'19. The aim is to illustrate the memory effect on the dynamics of COVID'19 with and without prevention measures through fractional calculus. Therefore, the structure of the model is in line with generalized proportional fractional derivative to assess the effects at each chronological change. Awareness about using medical mask, social distancing, frequent use of sanitizer or cleaning hand and supportive care during treatment are the strategies followed worldwide in this fight. Taking these into consideration, the optimal objective function proposed for the surveillance mitigation of COVID'19, is contemplated as the cost function. The effect analysis is supported through graphs and tabulated values. In addition, sensitivity inspection of basic reproduction number is also carried out with respect to different values of fractional index and cost function. Ultimately, social distancing and supportive care of infected are found to be significant in decreasing the basic reproduction number more rapidly.

Numerical simulation for the unsteady MHD flow and heat transfer of couple stress fluid over a rotating disk.

The present work is devoted to study the numerical simulation for unsteady MHD flow and heat transfer of a couple stress fluid over a rotating disk. A similarity transformation is employed to reduce the time dependent system of nonlinear partial differential equations (PDEs) to ordinary differential equations (ODEs). The Runge-Kutta method and shooting technique are employed for finding the numerical solution of the governing system. The influences of governing parameters viz. unsteadiness parameter, couple stress and various physical parameters on velocity, temperature and pressure profiles are analyzed graphically and discussed in detail.

Off-centered stagnation point flow of a couple stress fluid towards a rotating disk.

An investigation has been made to study the off-centered stagnation flow of a couple stress fluid over a rotating disk. The model developed for the governing problem in the form of partial differential equations has been converted to ordinary differential equations with the use of suitable similarity transformation. The analytical approximation has been made with the most promising analytical approach, homotopy analysis method (HAM). The convergence region of the obtained solution is determined and plotted. The effects of couple stress and nondimensional parameters have been observed on the flows of couple stress fluid. Also comparison has been made with the Newtonian fluid as the special case of considered problem.