Mathematical Modeling of Transmission Dynamics with Periodic Contact Rate and Control by Different Vaccination Rates of Hepatitis B Infection in Ghana

The paper evidenced that Hepatitis B infection is the world's deadliest liver infection and Vaccination is among the principal clinical strategies in fighting it. These have encouraged a lot of researchers to formulate mathematical models to accurately predict the mode of transmission and make deductions for better health decision-making processes. In this paper, an SEIR model is used to model the transmission of the Hepatitis B infection with periodic contact rate and examine the impact of vaccination. The model was validated using estimated data in Ghana and simulated in a MATLAB environment. The results showed that the vaccination rate has a great impact on the transmission mode of the Hepatitis B infection and the periodic contact rate may lead to a chaotic solution which could result in an uncontrolled spreading of the infection. It is concluded that even if the vaccination rate is 70%, the infection rate would reduce to the minimum barest so more newborns must be vaccinated.

Road to chaos in a Duffing oscillator with time delay loop

This article examines a single Duffing oscillator with a time delay loop. The research aims to check the impact of the time delay value on the nature of the solution, in particular the scenario of transition to a chaotic solution. Dynamic tools such as bifurcation diagrams, phase portraits, Poincaré maps, and FFT analysis will be used to evaluate the obtained results.

MATHEMATICAL MODEL OF THE SHOCK TREATMENT IN CARDIOLOGY

Chaotic solutions of the driven Dufng equation are very important and interesting for researchers in different areas. In many cases chaos has negative effect on complicated processes As we know, chaotic solution means that a small change in one state of a deterministic nonlinear system can result in large differences in a later state, meaning there is sensitive dependence on initial conditions. It happens in electric circuits, economics, meteorology and in the electrophysiology of the heart. Therefore the aim of the present paper to give a new insight on the chaos mitigation by shock.. It was found in the present work by means of the mathematical modeling that the shock-term indeed can mitigate chaos produced in the driven Dufng equation.

About the Transition to Turbulence Through Chaotic Distortion of Vortex Shedding

The results of direct numerical integration of the Navier-Stokes equations are evaluated against experimental data for the problem of flow around a hard sphere at rest. The evaluation is performed for both the sequence of vortex shedding regimes, replacing stable modes after the loss of stability, and the regime of turbulence replacing vortex shedding modes as Reynolds number Re increases. The evaluation demonstrates the unsuitability of classic hydrodynamics equations to interpret the phenomenon of vortex shedding. Moreover, the attainment of critical value of Re is accompanied by loss of the direction of instability development. Wrong direction of instability development results in the attainment of multiperiodic, that is, essentially chaotic, solution. Insurmountable discrepancies between calculation results and experimental data show that the chaotic deterministic solution to the Navier-Stokes equation is not suitable for interpretation of turbulence. An analogy is revealed between the sequence of modes observed in flow around a sphere as Re increases and sequence of modes in shear layer behind a cylinder with paraboloidal nose recorded while moving downstream along the contour of streamlined body. The conclusions are as follows. The turbulence of shear flow is regular unstable vortex shedding regime distorted by chaotic fluctuations. Solutions to the classic hydrodynamics equations are incapable of interpreting both regular and chaotic turbulence component. Multimoment hydrodynamics seeks for decision of these problems along the way toward an increase in the number of principle hydrodynamic values.

Can We Obtain a Reliable Convergent Chaotic Solution in any Given Finite Interval of Time?

Generally, it is difficult to obtain convergent chaotic solution in an arbitrarily given finite interval of time. Some researchers even believe that all chaotic responses are simply numerical noise and have nothing to do with solutions of differential equations. However, using 1200 CPUs of the National Supercomputer TH-A1 at Tianjin and a parallel integration algorithm of the so-called "Clean Numerical Simulation" (CNS) based on the 3500th-order Taylor expansion and data in 4180-digit multiple precision, one can obtain reliable convergent chaotic solution of the Lorenz equation in a rather long time interval [0,10 000]. This supports Lorenz's optimistic viewpoint [Lorenz 2008] that "numerical approximations can converge to a chaotic true solution throughout any finite range of time". It also supports Tucker's proof [Tucker 1999, 2002] for the famous Smale's 14th problem that the strange attractor of the Lorenz equation indeed exists.

Study on the Chaotic Behavior of Smoke Plumes and Fire Trends

The partial differential equations describing fire smoke plume is deduced from the general equation buoyant jet. Applied Lorenz model to study the chaotic behavior of smoke plumes, discussed the nature of evolution equations within the Prandtl number changes, at the same time the emergence of chaotic solutions for the numerical analysis. Smoke plumes appear chaotic, indicating that the flow state changes from the stable convection to unstable convection, at this condition may produce fire whirlwind, so that disaster to expand. Contact Fire actual process parameters when generating chaotic solution, we propose a disaster prediction and control of ideas.

A coupling successive approximation method for solving Duffing equation and its application

The paper proposes an algorithm to solve a general Duffing equation, in which a process of transforming the initial equation to a resulting equation is proposed, and then the coupling successive approximation method is applied to solve the resulting equation. By using this algorithm a special physical factor and complex-valued solutions to the general Duffing equation are revealed. The proposed algorithm does not use any assumption of small parameters in the equation solving. The coupling successive procedure provides an analytic approximated solution in both real-valued or complex-valued solution. The procedure also reveals a formula to evaluate the vibration frequency, \(\varphi\), of the non-linear equation. Since the first approximation solution is in a closed-form, the chaos index of the general Duffing equation and the chaotic characteristics of solutions can be predicted. Some examples are used to illustrate the proposed method. In the case of chaotic solution, the Pointcaré conjecture is used for solution verification.