Properties of a model of an epidemic for certain infectious diseases (Q1061653)

A six-dimensional system of ordinary differential equations, \[ \dot x=- \beta y'x/(x'+y')+\eta z,\quad \dot x'=-\beta 'yx'/(x+y)+\eta 'z', \] \[ \dot y=\beta y'x/(x'+y')-\gamma y,\quad \dot y'=\beta 'yx'/(x+y)-\gamma 'y', \] \[ \dot z=\gamma y-\eta z,\quad \dot z'=\gamma 'y'-\eta 'z', \] is proposed as a mathematical model of infectious diseases to predict the known properties of epidemics and to explore possibilities of epidemic control. The model assumes that the population is divided by sex into two distinct groups, which are termed group 1 and group 2. The values of the main variables for each of these two groups are denoted by x,y,z and x',y',z', respectively. The total number of individuals in each group is assumed constant, namely, \(x+y+z=N\) and \(x'+y'+z'=N'.\) Two essentially different cases of an epidemic are investigated. The first case is characterized by a relatively high proportion of identified cases given a high level of sporadic infection. The second case is characterized by a relatively low sickness rate, and the proportion of identified cases is also relatively low.