Numerical Analysis for the Effect of Irresponsible Immigrants on HIV/AIDS Dynamics

The human immunodeficiency viruses are two species of Lentivirus that infect humans.Over time,they cause acquired immunodeficiency syndrome,a condition in which progressive immune system failure allows life-threatening opportunistic infections and cancers to thrive.Human immunodeficiency virus infection came from a type of chimpanzee in Central Africa.Studies show that immunodeficiency viruses may have jumped from chimpanzees to humans as far back as the late 1800s.Over decades,human immunodeficiency viruses slowly spread across Africa and later into other parts of the world.The Susceptible-Infected-Recovered(SIR)models are significant in studying disease dynamics.In this paper,we have studied the effect of irresponsible immigrants on HIV/AIDS dynamics by formulating and considering different methods.Euler,Runge Kutta,and a Non-standardfinite difference(NSFD)method are developed for the same problem.Numerical experiments are performed at disease-free and endemic equilibria points at different time step sizes‘ℎ’.The results reveal that,unlike Euler and Runge Kutta,which fail for large time step sizes,the proposed Non-standardfinite difference(NSFD)method gives a convergence solution for any time step size.Our proposed numerical method is bounded,dynamically con-sistent,and preserves the positivity of the continuous solution,which are essential requirements when modeling a prevalent disease.

Optimality of Solution with Numerical Investigation for Coronavirus Epidemic Model

The novel coronavirus disease,coined as COVID-19,is a murderous and infectious disease initiated from Wuhan,China.This killer disease has taken a large number of lives around the world and its dynamics could not be controlled so far.In this article,the spatio-temporal compartmental epidemic model of the novel disease with advection and diffusion process is projected and analyzed.To counteract these types of diseases or restrict their spread,mankind depends upon mathematical modeling and medicine to reduce,alleviate,and anticipate the behavior of disease dynamics.The existence and uniqueness of the solution for the proposed system are investigated.Also,the solution to the considered system is made possible in a well-known functions space.For this purpose,a Banach space of function is chosen and the solutions are optimized in the closed and convex subset of the space.The essential explicit estimates for the solutions are investigated for the associated auxiliary data.The numerical solution and its analysis are the crux of this study.Moreover,the consistency,stability,and positivity are the indispensable and core properties of the compartmental models that a numerical design must possess.To this end,a nonstandard finite difference numerical scheme is developed to find the numerical solutions which preserve the structural properties of the continuous system.The M-matrix theory is applied to prove the positivity of the design.The results for the consistency and stability of the design are also presented in this study.The plausibility of the projected scheme is indicated by an appropriate example.Computer simulations are also exhibited to conclude the results.

Numerical Analysis of Novel Coronavirus (2019-nCov) Pandemic Model with Advection

Recently,the world is facing the terror of the novel corona-virus,termed as COVID-19.Various health institutes and researchers are continuously striving to control this pandemic.In this article,the SEIAR(susceptible,exposed,infected,symptomatically infected,asymptomatically infected and recovered)infection model of COVID-19 with a constant rate of advection is studied for the disease propagation.A simple model of the disease is extended to an advection model by accommodating the advection process and some appropriate parameters in the system.The continuous model is transposed into a discrete numerical model by discretizing the domains,finitely.To analyze the disease dynamics,a structure preserving non-standard finite difference scheme is designed.Two steady states of the continuous system are described i.e.,virus free steady state and virus existing steady state.Graphical results show that both the steady states of the numerical design coincide with the fixed points of the continuous SEIAR model.Positivity of the state variables is ensured by applying the M-matrix theory.A result for the positivity property is established.For the proposed numerical design,two different types of the stability are investigated.Nonlinear stability and linear stability for the projected scheme is examined by applying some standard results.Von Neuman stability test is applied to ensure linear stability.The reproductive number is described and its pivotal role in stability analysis is also discussed.Consistency and convergence of the numerical model is also studied.Numerical graphs are presented via computer simulations to prove the worth and efficiency of the quarantine factor is explored graphically,which is helpful in controlling the disease dynamics.In the end,the conclusion of the study is also rendered.