In this paper, we propose and analyze a mathematical model describing the effect of awareness programs by public media on the prevalence of Typhoid fever. A threshold quantity $R_{0}$, similar to the basic reproduction number is derived. We investigate the biologically meaningful equilibrium points and their local stability analysis. The global stability analysis has been performed with respect...

We consider a mathematical model of epidemic spread  in which the  population  is partitioned  into five compartments of susceptible S(t), Infected I(t), Removed R(t), Prevented U(t) and the Controlled W(t). We assume each of the compartments comprises of cohorts of individuals which are  identical with respect to the disease status. We derive five systems of equations to represent each of the ...

We define belief-free equilibria in two-player games with incomplete information as sequential equilibria for which players’ continuation strategies are best-replies, after every history, independently of their beliefs about the state of nature. We characterize a set of payoffs that includes all belief-free equilibrium payoffs. Conversely, any payoff in the interior of this set is a belief-free...

In  this  paper a  non-linear  model  with  fractional  order  is  presented  for  analyzing  and  controlling the  spread  of  HIV virus.  Both  the  disease-free  equilibrium and the endemic equilibrium are  found  and  their  stability is  discussed. The basic reproduction number , which is a function of the constant parameters in the model, plays an essential  role in the stability of  the ...

In this paper, an SIR epidemic model with an infectious period and a non-linear Beddington-DeAngelis type incidence rate function is considered. The dynamics of this model depend on the reproduction number R0. Accurately, if R0 < 1, we show the global asymptotic stability of the disease-free equilibrium by analyzing the corresponding characteristic equation and using compa...

A recent paper Ncube (2013) [11] considered the disease-free equilibrium in a mathematical model for intra-host dynamics of Plasmodium falciparum malaria with discrete immune time delay. The author showed that depending on system parameters, the disease-free steady state can be absolutely stable (i.e. asymptotically stable for arbitrary positive values of the time delay), or it can be asymptoti...

Imaging with spoiled, balanced or nonbalanced gradient echo (GRE) refers to a class of fast imaging sequences that use a dynamic equilibrium or steady state signal for imaging. As originally introduced in 1958 by Carr (1) for NMR spectroscopy, a dynamic equilibrium or steadystate can be established by a train of radio-frequency (RF) excitation pulses interleaved by periods of ‘free precession’,...

The approach to equilibrium, from a nonequilibrium initial state, in a system at its critical point is usually described by a scaling theory with a single growing length scale, xi(t) approximately t(1/z), where z is the dynamic exponent that governs the equilibrium dynamics. We show that, for the 2D XY model, the rate of approach to equilibrium depends on the initial condition. In particular, x...

Consider an equilibrium reaction aA+ bB ⇀↽ cC+ dD We do not specify any phases, as we will treat the reaction generally using activities. An equilibrium reaction is one that can proceed in both directions, as indicated by the ⇀↽ symbol replacing the usual −→ in the chemical equation. Recall that the molar free energy ∆Ḡj for compound j in the reaction in terms of its activity aj as ∆Ḡ = ∆Ḡ◦ +RT...