On the existence and uniqueness of solutions for implicit linear systems on finite interval

Dynamics of an Infectious Disease Where Media Coverage Influences Transmission

“…which is positively invariant and attracting, and over the allowed domain, the model is well defined [38]. If recovery is nonpermanent, then, (1a) now reads…”

“…This is an implicitly defined system for which the problem of the existence and uniqueness of solutions on a finite time interval has been studied by Banaszuk [38]. M(t) is the signal function capturing the media coverage over time, Λ is the rate at which susceptible individuals are recruited into the population (no recruitment of infective individuals occurs), Λ is the constant recruitment rate, β is the baseline contact rate, λ = β(I + H)/N is the force of infection, ∈ [0, 1) is the modification parameter that accounts for the reduction in transmissibility of individuals under treatment, μ is the natural death rate, α I and α H are the death rates due to the disease and when under treatment, respectively, (α I > α H ), τ is the rate at which individuals enter the health care settings seeking for treatment [23], and δ H is the recovery rate.…”