We formulate a deterministic epidemic model for the spread of Corona Virus Disease . We have included asymptomatic, quarantine and isolation compartments in the model, as studies have stressed upon the importance of these population groups on the transmission of the disease. We calculate the basic reproduction number R 0 and show that for R 0 < 1 the disease dies out and for R 0 > 1 the disease is endemic. Using sensitivity analysis we establish that R 0 is most sensitive to the rate of quarantine and isolation and that a high level of quarantine needs to be maintained as well as isolation to control the disease. Based on this we devise optimal quarantine and isolation strategies, noting that high levels need to be maintained during the early stages of the outbreak. Using data from the Wuhan outbreak, which has nearly run its course we estimate that R 0 = 1.87 which while in agreement with other estimates in the literature is on the lower side.

Ebola virus disease (EVD) has emerged as a rapidly spreading potentially fatal disease. Several studies have been performed recently to investigate the dynamics of EVD. In this paper, we study the transmission dynamics of EVD by formulating an SEIR-type transmission model that includes isolated individuals as well as dead individuals that are not yet buried. Dynamical systems analysis of the model is performed, and it is consequently shown that the disease-free steady state is globally asymptotically stable when the basic reproduction number, [Formula: see text] is less than unity. It is also shown that there exists a unique endemic equilibrium when [Formula: see text]. Using optimal control theory, we propose control strategies, which will help to eliminate the Ebola disease. We use data fitting on models, with and without isolation, to estimate the basic reproductive numbers for the 2014 outbreak of EVD in Liberia and Sierra Leone.

A major link or node failure in a network can severely affect services offered by the network. In this paper; we address network perfomnce, especially, in the event of a link failure in the presence of both unicast and multicast muting in wide-area datagram networks, such as the Intemet. Since various services can exert different workloads (per connectiodsession), we have developed workloads to reflect both one-to-many and many-to-many multicast communications on top of multicast routing. Through network simulation, we quantify effects on how unicast services and multicast services are affected due to such a failure.

A cell growth model for a size‐structured cell population with a stochastic growth rate for size and division into two daughter cells of unequal size is studied in this paper. The model entails an initial boundary value problem that involves a second‐order parabolic partial differential equation with two nonlocal terms, the presence of which is a consequence of asymmetry in the cell division. The solution techniques for solving such problems are rare due to the nonlocal terms. In this paper, we solve the initial boundary value problem for arbitrary initial distributions. We obtain a separable solution, as well as the general solution to the partial differential equation, and show that the solutions converge to the separable solution for large time. As in the symmetric division case, the dispersion term does not affect the rate of convergence to the separable solution.

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