A Modified Discrete SIR Model

Zeroth-Order Deterministic Local and Delay Pandemic Model Comparison

“…Of course, the inflection time > was taken from the numerical result. Changing boundary conditions simply shifts the curves in time leaving their shapes invariant as with the approximation in Equation (11). Also, the soliton solution cannot reproduce the fine details in the curves near t = 0 where the boundary function is important.…”

“…As detailed below, the boundary conditions, I(t) and S(t) over this early interval, are determined by the distribution in the exposure times of the initially exposed or infected who trigger the pandemic. Equations (3-6) specialized to a Delay SIR model are identical to the model discussed in References [11, 12, 15], neglecting natural birth and death.…”

“…Less common are models [1, 5, 10-12, 14, 15] which specify the rates of change in the populations at a given time in terms of populations at an earlier time. Specifically, this paper considers a pandemic model similar to the traditional SEIR Model (including SIR) constructed by specifying the incubation time τ δ (for example, 5 days) an individual spends prior to becoming infectious and the total time τ γ (e.g., 20 days) to recovery.…”

Population dynamics of a non-cultivated biennial plant Tragopogon pratensis infected by the autoecious demicyclic rust fungus Puccinia hysterium

“…Such compartmentalised models of disease dynamics have been used previously to represent plant -fungal pathogen dynamics in continuous time (Gilligan, 2002). The model developed here is an example where a discrete-time approach (Allen 1994;Switkes, 2003) provides a more appropriate representation of the host-pathogen system, given the biennial host characteristics, the unusual yet key systemic nature of the rust pathogen, and the infection process linking second and first year plants. Expanded forms of the discrete SIR model have been used to describe gene frequency and disease spread in plant populations (Kesinger et al, 2001).…”

Application of the Lambert W Function to the SIR Epidemic Model

“…The SIR model assumes: (i) The rate at which susceptibles become infected is κ S(t)I (t), where the transmission coefficient κ is a constant; (ii) the rate of transition from the infected class to the removed class is given by I (t), where the constant 1/ is the average length of the infectious period [1,2,5,7]. With these assumptions, the differential equations describing the number of individuals in the three classes are…”