Impact of information intervention on stochastic hepatitis B model and its variable-order fractional network

Abstract

This paper aims at analyzing the dynamical behavior of a SIR hepatitis B epidemic stochastic model via a novel approach by incorporating the effect of information interventions and random perturbations. Initially, we demonstrate the positivity and global existence of the solutions. Afterward, we derive the stochastic threshold parameter Rs, followed by the fact that this number concludes the transmission of hepatitis B from the population. By increasing the intensity of noise, we get Rs less than one, inferring that ultimately hepatitis B will lapse. While decreasing the intensity of noise to a sufficient level, we have Rs > 1. For the case Rs > 1, adequate results for the presence of stationary distribution are achieved, showing the prevalence of hepatitis B. The present study also involves the derivation of the necessary conditions for the persistence of the epidemic. Finally, the main theoretical solutions are plotted through simulations. Discussion on theoretical and numerical results shows that utilizing random perturbations and information interventions have a pronounced impact on the syndrome's dynamics. Furthermore, since most communities interact with each other, and the disease spread rate is affected by this factor, a new variable-order fractional network of the stochastic hepatitis B model is offered. Subsequently, this study will provide a robust theoretical basis for comprehending worldwide SIR stochastic and variable-order fractional network-related case studies.

A stochastically perturbed co-infection epidemic model for COVID-19 and hepatitis B virus

“…Describe all the parameters in Table 1 while the governing equations describing transitions in the model are given in Eq. (1). Besides, the following assumptions were taken into consideration while formulating the model: The rates of recovery from the diseases are taken at the rates α 1 , γ 1 and η 1 , for HBV, SARS-CoV-2 and co-infection individuals, respectively.…”

“…In the section, we intend to discuss the analysis of existence, boundedness and uniqueness of positive solution and deterministic stability of model (1), for this purpose using the classical theory of ODE's [26][27][28], and we will focus on the conditions which guarantee the local asymptotic and the global stability's of equilibriums.…”

“…COVID-19 vaccinations were recently approved to help stop the spread of the virus. The vaccine’s use, however, is still in its early stages of distribution and uptake [ 1 , 2 ]. Likewise, hepatitis B is also one of the contagious diseases of the liver and more than 3.5 billion of the population are infected chronically around the world [ 3 ], in which 25-40% are carriers developing cirrhosis hepatocellular carcinoma and liver disease [ 4 ].…”

Application of variable-order fractional calculus in neural networks: where do we stand?

“…Since the fractional calculus is a generalized form of the integer one and can capture many time-dependent phenomena, it is a more practical and precise approach to the use of the fractional models, especially with time-varying fractional order. Considering this point, in the current collection, some studies have investigated modeling and dynamical investigation of neural networks using variable-order fractional calculus [11][12][13][14][15][16].…”

Backward bifurcation and optimal control in a co-infection model for SARS-CoV-2 and ZIKV

“…Mathematical modelling has become an important tool for studying the dynamics of infectious diseases [6] , [7] , [8] , [9] , [10] , [11] , [12] . Several models have been developed to study the dynamics of SARS-CoV-2 [13] , [14] , [15] , [16] , [17] .…”