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Thus, a more highly infectious disease has a higher ��. The number �� is the rate of recovery, so that 1/�� is the average time period during which an infected individual remains infectious. The product ��S(t)?I(t) is the total infection rate, the fraction of the population that will be infected per unit time at time t. To understand this, note that, if a fraction I(t) GSK126 cost of the population is currently infected, then they would infect a fraction ��I(t) of the population per unit time if all of their contacts were with susceptible individuals, but as only a fraction S(t) of the population is currently susceptible, they will only infect ��I(t)?S(t) per unit time. The ratio ��/�� is also known as the basic reproductive number R0, which is an important index for quantifying the transmission of pathogens. R0 is defined as the average number of people infected by an infected individual over the disease infectivity period, in a totally susceptible population. This simple model, which is the basis for many elaborations, turns out to provide some quite striking predictions. By entering the above differential equations into any software for the numerical solution of differential equations, and choosing some values for �� and �� together with the initial values S(0), I(0), and R(0), it is possible to generate an epidemic curve corresponding to this model, that is a prediction for the fraction of the population that will be infected on each day of the epidemic. Moreover, analytical tools allow us to draw some general conclusions about the model's solutions. The most important conclusions are as follows: The epidemic Transducin threshold: if the inequality S(0) R0?>?1 holds, then the number of infected individuals will rapidly selleck chemical decrease; that is, no epidemic will occur. Note that, if S(0) R0?>?1, then an epidemic will occur, no matter how small the initial number of infected individuals. The size of the epidemic, when it occurs, will not depend on the initial number of infectives, but it will depend on the initial fraction of susceptibles, S(0), and on R0. An important point here is that the final size of the epidemic (the fraction of the population infected) will always be strictly smaller than the initial fraction of the population that was susceptible, S(0), so that there will always remain a subpopulation of susceptible individuals who have not been infected. These conclusions, in so far as they apply in reality, have some crucial implications. Most notably, the epidemic threshold implies that, if we vaccinate a fraction of the population prior to the arrival of the pathogen, so as to reduce the initial fraction of susceptibles to S(0)?