In epidemiology, the<unk>  is used to derive the basic reproduction number, for a compartmental model of the spread of infectious diseases. In population dynamics it is used to compute the basic reproduction number for structured population models. It is also used in multi-type branching models for analogous computations. The method to compute the basic reproduction ratio using the<unk>  is given by Diekmann et al. (1990) and van den Driessche and Watmough (2002). To calculate the basic reproduction number by using a<unk> , the whole population is divided into compartments in which there are infected compartments. Let be the numbers of infected individuals in the infected compartment at time t. Now, the epidemic model is :, where In the above equations, represents the rate of appearance of new infections in compartment . represents the rate of transfer of individuals into compartment by all other means, and represents the rate of transfer of individuals out of compartment . The above model can also be written as : where : and : Let be the disease-free equilibrium. The values of the Jacobian<unk> es and are: : and : respectively. Here, and are m × m<unk> es, defined as and . Now, the<unk>  is known as the<unk> . The largest modulus of the eigenvalues or spectral radius of is the basic reproduction number of the model.
Next-generation matrix
QTY Code
Independent SAGE
Triage tag
NDR Method
In silico medicine
EFAR System Model
Bioanalysis