The Complex Dynamics of Hepatitis B Infected Individuals with Optimal Control

Abstract

This paper proposes various stages of the hepatitis B virus (HBV) besides its transmissibility and nonlinear incidence rate to develop an epidemic model. The authors plan the model, and then prove some basic results for the well-posedness in term of boundedness and positivity. Moreover, the authors find the threshold parameter R0, called the basic/effective reproductive number and carry out local sensitive analysis. Furthermore, the authors examine stability and hence condition for stability in terms of R0. By using sensitivity analysis, the authors formulate a control problem in order to eradicate HBV from the population and proved that the control problem actually exists. The complete characterization of the optimum system was achieved by using the 4 th-order Runge-Kutta procedure.

Transmission dynamics of COVID-19 pandemic with combined effects of relapse, reinfection and environmental contribution: A modeling analysis

“…In this part, numerical simulations were carried out to explain the theoretical results given in the previous sections as well as to gain deeper insight into the COVID-19 dynamic transmission behaviour. To obtain numerical solutions to the proposed model, we employed the Euler framework to find the graphical results using parameter values from Table 2 [8] , [9] , [10] , [11] , [75] , [76] , [77] . The procedure is as follows: Suppose the initial condition, which is well-posed, is given below.…”

On the analysis of Caputo fractional order dynamics of Middle East Lungs Coronavirus (MERS-CoV) model

“…The largest MERS-CoV transmission from human to human was first time formulated by Assire et al [7] . The animal to human transmission is due to indirect exposition was described by Zumla et al [8] . They also analyzed the said transmission caused by the taking non-pasteurized milk of the camels in the middle Eastern countries.…”

On a Coupled System of Fractional Differential Equations via the Generalized Proportional Fractional Derivatives

“…The theory of fractional calculus has become an attractive area of research for mathematicians and physicians because of its fertile aspects in many applications in natural science [1,2], engineering [3], and many other fields. Moreover, the fractional differential equations have been employed successfully in the modeling of many biological problems, for example, human liver [4], hepatitis B [5][6][7], mumps virus [8] and methanol detoxification in the human body [9], and other differential models in thermodynamic and physics such as thermostat [10], pantograph [11], diffusion-wave system [12], and dynamical systems [13]. For additional specifics about the theory of fractional calculus and applications, we suggest the books of Kilbas et al [14], Podlubny [15], and Samko et al [16].…”