Some discrete-time SI, SIR, and SIS epidemic models

On a discrete West Nile epidemic model

“…Discrete time epidemic models have been studied by Allen [1,2], Lewis et al [15], Thomas and Urena [17], and more recently by Franke [9] on periodic epidemic models. In [1,2], the models are expressed in terms of time unit t and nonnegativity of the solutions are derived using the quantity t and model parameters.…”

“…Discrete time epidemic models have been studied by Allen [1,2], Lewis et al [15], Thomas and Urena [17], and more recently by Franke [9] on periodic epidemic models. In [1,2], the models are expressed in terms of time unit t and nonnegativity of the solutions are derived using the quantity t and model parameters. Since data for the West Nile epidemics given in the literature [3,5,7,10,16] are in terms of days, our time unit is taken to be a day and model (2.1) does not involve time unit t as in [1,2].…”

“…In [1,2], the models are expressed in terms of time unit t and nonnegativity of the solutions are derived using the quantity t and model parameters. Since data for the West Nile epidemics given in the literature [3,5,7,10,16] are in terms of days, our time unit is taken to be a day and model (2.1) does not involve time unit t as in [1,2]. We now impose the following conditions on the parameters so that solutions of (2.1) will remain nonnegative as shown in Proposition 2.1.…”

Discrete-Time S-I-S Models With Simple and Complex Population Dynamics

“…System (1), is an extension of the discretetime (S-I-S) epidemic models of Barrera et al and Velazquez [6,27]. (2) that is, Equation (2) models the dynamics (demography) of the total population.…”

“…Theoretical studies of ( S -I -S) epidemic models have been carried out in deterministic (discrete and continuous-time) and stochastic Markov chains for a long time (see Allen [1,2]; Anderson et al [3]; Bailey [5]; Castillo et al [7 -10]; Cooke and Yorke [11]; Hassell et al [18] and Nasell [23], to name a few). Barrera et al [6]; Velazquez [27]; and Castilla-Chavez and Yakubu [9,10] have developed models for the study of disease dynamics in populations with discrete generations and potentially complex (chaotic) disease-free dynamics.…”