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Algorithmic approach for an unique definition of the next generation matrix
We also present examples where other choices may be more reasonable, with more terms in F, or more terms in V .
Explicit mathematical epidemiology results on age renewal kernels and R0 formulas are often consequences of the rank one property of the next generation matrix
A very large class of ODE epidemic models (2. 2) discussed in this paper enjoys the property of admitting also an integral renewal formulation, with respect to an "age of infection kernel" a(t) which has a matrix exponential form (3. 2).
New results and open questions for SIR-PH epidemic models with linear birth rate, loss of immunity, vaccination, and disease and vaccination fatalities
The literature suggests that it is impossible to find general laws concerning the endemic points.
Stability analysis of an eight parameter SIR-type model including loss of immunity, and disease and vaccination fatalities
We revisit here a landmark five parameter SIR-type model of [DvdD93, Sec.
A review of matrix SIR Arino epidemic models
Many of the models used nowadays in mathematical epidemiology, in particular in COVID-19 research, belong to a certain sub-class of compartmental models whose classes may be divided into three "(x, y, z)" groups, which we will call respectively "susceptible/entrance, diseased, and output" (in the classic SIR case, there is only one class of each type).
Optimizing dividends and capital injections limited by bankruptcy, and practical approximations for the Cramér-Lundberg process
The recent papers Gajek-Kucinsky(2017) and Avram-Goreac-Li-Wu(2020) investigated the control problem of optimizing dividends when limiting capital injections stopped upon bankruptcy.
Optimization and Control Probability
