An SIR model with distributed delay and a general incidence function is studied. Conditions are given under which the system exhibits threshold behaviour: the disease-free equilibrium is globally asymptotically stable if R0 is less than 1 and globally attracting if R0=1; if R0 is larger than 1, then the unique endemic equilibrium is globally asymptotically stable. The global stability proofs us...

Some annulus oscillation criteria are established for the second order damped elliptic differential equation N X i,j=1 Di[aij(x)Djy] + N X i=1 bi(x)Diy + C(x, y) = 0 under quite general assumption that they are based on the information only on a sequence of annuluses of Ω(r0) rather than on the whole exterior domain Ω(r0). Our results are extensions of those due to Kong for ordinary differentia...

In this paper, a HTLV-I infection model with CTL response is considered. To account for a series of events in infection process, we incorporate a intracellular time delay in the model. We prove that the global dynamics are determined by two threshold parameters R0 and R1, basic reproduction numbers for viral infection and for CTL response, respectively. If R0 < 1, the infection-free equilibrium...

A recent work of Schmidt and Springborg on one-dimensional chains of metal atoms has prompted us to use a quantum-chemical model, posed in terms of dimer potential energy curves, to analyze equlibrium near-neighbour distances r0 as a function of local coordination number c. For five monoatomic metal atoms, H, K, Al, Pb and Bi, values of r0 are available for three or more different lattices. The...

This paper addresses a modified epidemic model with saturated incidence and incomplete treatment. The existence of all equilibrium points is analyzed. A reproduction number R0 determined. Next, it found that the non-endemic point P0 stable in case R0&lt;1, but unstable R0&gt;1. special conditions to analyze local global stability endemic are investigated. Globally, sensitivity analysis system s...

We compute the deflection angle for a light ray traveling in a flat ΛCDM cosmology which encounters a completely condensed mass region to second order inm/r0 and first order inm/r0×Λr 2 0.We find that the most significant correction to the Einstein angle occurs not because of the non-linear terms but instead because the condensed mass is embedded in an expanding cosmology. We predict a decrease...

Let R = ⊕ d∈N0 Rd be a positively graded commutative Noetherian ring which is standard in the sense that R = R0[R1], and set R+ := ⊕ d∈N Rd, the irrelevant ideal of R. (Here, N0 and N denote the set of non-negative and positive integers respectively; Z will denote the set of all integers.) Let M = ⊕ d∈Z Md be a non-zero finitely generated graded R-module. This paper is concerned with the behavi...

I discuss the so-called SuperSpreader (SS) epidemic, for which SARS is the canonical example (and, perhaps, MERS will be another). I use simulation by an agent-based model as well as the mathematics of multi-type branchingprocesses to illustrate how the SS epidemic differs from the more-familiar uniform epidemic (e.g., caused by influenza). The conclusions may surprise the reader: (a) the SS ep...