The minimal solution of a Markov renewal equation

1990 ◽  
Vol 3 (4) ◽  
pp. 579-585
Author(s):  
Haiyan Cai
1980 ◽  
Vol 10 (4) ◽  
pp. 12-13
Author(s):  
Walter R. Nunn
Keyword(s):  

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Bo Zhu ◽  
Baoyan Han

A class of backward doubly stochastic differential equations (BDSDEs) are studied. We obtain a comparison theorem of these multidimensional BDSDEs. As its applications, we derive the existence of solutions for this multidimensional BDSDEs with continuous coefficients. We can also prove that this solution is the minimal solution of the BDSDE.


2015 ◽  
Vol 14 (1) ◽  
pp. 134-144 ◽  
Author(s):  
C.J. Coelho ◽  
D. Molin ◽  
H.A. Wood Joris ◽  
E.F. Caires ◽  
J.R. Gardingo ◽  
...  

2021 ◽  
Vol 8 (4) ◽  
Author(s):  
Francesca Scarabel ◽  
Lorenzo Pellis ◽  
Nicholas H. Ogden ◽  
Jianhong Wu

We propose a deterministic model capturing essential features of contact tracing as part of public health non-pharmaceutical interventions to mitigate an outbreak of an infectious disease. By incorporating a mechanistic formulation of the processes at the individual level, we obtain an integral equation (delayed in calendar time and advanced in time since infection) for the probability that an infected individual is detected and isolated at any point in time. This is then coupled with a renewal equation for the total incidence to form a closed system describing the transmission dynamics involving contact tracing. We define and calculate basic and effective reproduction numbers in terms of pathogen characteristics and contact tracing implementation constraints. When applied to the case of SARS-CoV-2, our results show that only combinations of diagnosis of symptomatic infections and contact tracing that are almost perfect in terms of speed and coverage can attain control, unless additional measures to reduce overall community transmission are in place. Under constraints on the testing or tracing capacity, a temporary interruption of contact tracing may, depending on the overall growth rate and prevalence of the infection, lead to an irreversible loss of control even when the epidemic was previously contained.


1992 ◽  
Vol 57 (1) ◽  
pp. 91-97
Author(s):  
Janusz Traple

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