The basic reproduction number, R0, is often defined as the average number of infections generated by a newly infected individual in a fully susceptible population. The interpretation, meaning, and derivation of R0 are controversial. However, in the context of mean field models, R0 demarcates the epidemic threshold below which the infected population approaches zero in the limit of time. In this...

An AC voltmeter is a device that measures the (peak) oscillating current I0 across a large resistor R0 that is attached to leads whose tips, 1 and 2, may be connected to some other circuit. The reading of the voltmeter (if properly calibrated) is Vmeter = I0(R0 + Rleads) where Rleads R0. AC voltmeters typically report the root-mean-square voltage Vrms = I0(R0 +Rleads)/ √ 2 rather than I0(R0 +Rl...

We consider the expected residual minimization formulation of the stochastic R0 matrix linear complementarity problem. We show that the involved matrix being a stochastic R0 matrix is a necessary and sufficient condition for the solution set of the expected residual minimization problem to be nonempty and bounded. Moreover, local and global error bounds are given for the stochastic R0 matrix li...

Clustering of cosmic-ray sources affects the flux observed beyond the cutoff imposed by the cosmic microwave background and may be important in interpreting the AGASA, Fly’s Eye, and HiRes data. The standard deviation, σ, in the predicted number, N , of events above 10 eV is σ/N = 0.9(r0/10Mpc) 0.9, where r0 is the unknown scale length of the correlation function (r0 ≃ 10 Mpc for field galaxies...

The concept of the basic reproduction number (R0) occupies a central place in epidemic theory. The value of R0 determines the proportion of the population that becomes infected over the course of a (modelled) epidemic. In many models, (i) an endemic infection can persist only if R0>1, (ii) the value of R0 provides a direct measure of the control effort required to eliminate the infection, and (...

A model of the Galaxy with outer ring R1R2 can explain observed distribution radial, VR, and azimuthal, VT, velocity components along Galactocentric distance, R, derived from Gaia EDR3 data. We selected stars catalogue reliable parallaxes, proper motions line-of-sight velocities lying near Galactic plane, |z|<200 pc, in sector Galactocentic angles |theta|<15 degrees calculated median VR VT smal...

A precise definition of the basic reproduction number, R0, is presented for a general compartmental disease transmission model based on a system of ordinary differential equations. It is shown that, if R0<1, then the disease free equilibrium is locally asymptotically stable; whereas if R0>1, then it is unstable. Thus, R0 is a threshold parameter for the model. An analysis of the local centre ma...

In this work we formulate and analyze a mathematical model for the transmission of West Nile Virus (WNV) infection between vector (mosquito) and avian population. We find the Basic Reproductive Number R0 in terms of measurable epidemiological and demographic parameters. R0 is the threshold condition that determines the dynamics of WNV infection: if R0< or =1 the disease fades out, and for R0 >1...

The prospects for the success of malaria control depend, in part, on the basic reproductive number for malaria, R0. Here, we estimate R0 in a novel way for 121 African populations, and thereby increase the number of R0 estimates for malaria by an order of magnitude. The estimates range from around one to more than 3,000. We also consider malaria transmission and control in finite human populati...

Ebola Virus Disease (EVD) is an infectious disease with a high mortality rate which caused by the virus from family of Filoviridae, genus Ebolavirus. Therefore, this research works on developing model spread SLSHVEQIHR type. The purpose study to analyze treatments, are quarantine and vaccination. Then determine equilibrium point basic reproduction number (R0). There two points, free endemic poi...