A NOVEL STOCHASTIC HEPATITIS B VIRUS EPIDEMIC MODEL WITH SECOND-ORDER MULTIPLICATIVE α-STABLE NOISE AND REAL DATA

This work presents an advanced and detailed analysis of the mechanisms of hepatitis B virus(HBV)propagation in an environment characterized by variability and stochas-ticity.Based on some biological features of the virus and the assumptions,the corresponding deterministic model is formulated,which takes into consideration the effect of vaccination.This deterministic model is extended to a stochastic framework by considering a new form of disturbance which makes it possible to simulate strong and significant fluctuations.The long-term behaviors of the virus are predicted by using stochastic differential equations with second-order multiplicative α-stable jumps.By developing the assumptions and employing the novel theoretical tools,the threshold parameter responsible for ergodicity(persistence)and extinction is provided.The theoretical results of the current study are validated by numerical simulations and parameters estimation is also performed.Moreover,we obtain the following new interesting findings:(a)in each class,the average time depends on the value ofα;(b)the second-order noise has an inverse effect on the spread of the virus;(c)the shapes of population densities at stationary level quickly changes at certain values of α.The last three conclusions can provide a solid research base for further investigation in the field of biological and ecological modeling.

Stochastic optimal control for norovirus transmission dynamics by contaminated food and water

Norovirus is one of the most common causes of viral gastroenteritis in the world,causing significant morbidity,deaths,and medical costs.In this work,we look at stochastic modelling methodologies for norovirus transmission by water,human to human transmission and food.To begin,the proposed stochastic model is shown to have a single global positive solution.Second,we demonstrate adequate criteria for the existence of a unique ergodic stationary distribution R0 s>1 by developing a Lyapunov function.Thirdly,we find sufficient criteria Rs<1 for disease extinction.Finally,two simulation examples are used to exemplify the analytical results.We employed optimal control theory and examined stochastic control problems to regulate the spread of the disease using some external measures.Additional graphical solutions have been produced to further verify the acquired analytical results.This research could give a solid theoretical foundation for understanding chronic communicable diseases around the world.Our approach also focuses on offering a way of generating Lyapunov functions that can be utilized to investigate the stationary distribution of epidemic models with nonlinear stochastic disturbances.

Discrete mass conservation and stability analysis of the ocean-atmosphere model with coupling conditions

In this work we considered bi-domain partial differential equations(PDEs)with two coupling interface conditions.The one domain is corresponding to the ocean and the second is to the atmosphere.The two coupling conditions are used to linked the interaction between these two regions.As we know that almost every engineering problem modeled via PDEs.The analytical solutions of these kind of problems are not easy,so we use numerical approximations.In this study we discuss the two essential properties,namely mass conservation and stability analysis of two types of coupling interface conditions for the oceanatmosphere model.The coupling conditions arise in general circulation models used in climate simulations.The two coupling conditions are the Dirichlet-Neumann and bulk interface conditions.For the stability analysis,we use the Godunov-Ryabenkii theory of normal-mode analysis.The main empha-sis of this work is to study the numerical properties of coupling conditions and an important point is to maintain conservativity of the overall scheme.Furthermore,for the numerical approximation we use two methods,an explicit and implicit couplings.The implicit coupling have further two algorithms,monolithic algorithm and partitioned iterative algorithm.The partitioned iterative approach is complex as compared to the monolithic approach.In addition,the comparison of the numerical results are exhibited through graphical illustration and simulation results are drafted in tabular form to validate our theoretical investigation.The novel characteristics of the findings from this paper can be of great importance in science and ocean engineering.