For decades,mathematical models of disease transmission have provided researchers and public health officials with critical insights into the progression,control,and prevention of disease spread.Of these models,one of...For decades,mathematical models of disease transmission have provided researchers and public health officials with critical insights into the progression,control,and prevention of disease spread.Of these models,one of the most fundamental is the SIR differential equation model.However,this ubiquitous model has one significant and rarely acknowledged shortcoming:it is unable to account for a disease's true infectious period distribution.As the misspecification of such a biological characteristic is known to significantly affect model behavior,there is a need to develop new modeling approaches that capture such information.Therefore,we illustrate an innovative take on compartmental models,derived from their general formulation as systems of nonlinear Volterra integral equations,to capture a broader range of infectious period distributions,yet maintain the desirable formulation as systems of differential equations.Our work illustrates a compartmental model that captures any Erlang distributed duration of infection with only 3 differential equations,instead of the typical inflated model sizes required by traditional differential equation compartmental models,and a compartmental model that captures any mean,standard deviation,skewness,and kurtosis of an infectious period distribution with 4 differential equations.The significance of our work is that it opens up a new class of easyto-use compartmental models to predict disease outbreaks that do not require a complete overhaul of existing theory,and thus provides a starting point for multiple research avenues of investigation under the contexts of mathematics,public health,and evolutionary biology.展开更多
This paper analyzes a finite-buffer renewal input single server discrete-time queueing system with multiple working vacations. The server works at a different rate rather than completely stopping working during the mu...This paper analyzes a finite-buffer renewal input single server discrete-time queueing system with multiple working vacations. The server works at a different rate rather than completely stopping working during the multiple working vacations. The service times during a service period, service time during a vacation period and vacation times are geometrically distributed. The queue is analyzed using the supplementary variable and the imbedded Markov-chain techniques. We obtain steady-state system length distributions at pre-arrival, arbitrary and outside observer＇s observation epochs. The analysis of actual waiting-time distribution and some performance measures are carried out. We present some numerical results and discuss special cases of the model.展开更多
基金SG was partially supported by the National Science Foundation Grant DMS-2052592.
文摘For decades,mathematical models of disease transmission have provided researchers and public health officials with critical insights into the progression,control,and prevention of disease spread.Of these models,one of the most fundamental is the SIR differential equation model.However,this ubiquitous model has one significant and rarely acknowledged shortcoming:it is unable to account for a disease's true infectious period distribution.As the misspecification of such a biological characteristic is known to significantly affect model behavior,there is a need to develop new modeling approaches that capture such information.Therefore,we illustrate an innovative take on compartmental models,derived from their general formulation as systems of nonlinear Volterra integral equations,to capture a broader range of infectious period distributions,yet maintain the desirable formulation as systems of differential equations.Our work illustrates a compartmental model that captures any Erlang distributed duration of infection with only 3 differential equations,instead of the typical inflated model sizes required by traditional differential equation compartmental models,and a compartmental model that captures any mean,standard deviation,skewness,and kurtosis of an infectious period distribution with 4 differential equations.The significance of our work is that it opens up a new class of easyto-use compartmental models to predict disease outbreaks that do not require a complete overhaul of existing theory,and thus provides a starting point for multiple research avenues of investigation under the contexts of mathematics,public health,and evolutionary biology.
文摘This paper analyzes a finite-buffer renewal input single server discrete-time queueing system with multiple working vacations. The server works at a different rate rather than completely stopping working during the multiple working vacations. The service times during a service period, service time during a vacation period and vacation times are geometrically distributed. The queue is analyzed using the supplementary variable and the imbedded Markov-chain techniques. We obtain steady-state system length distributions at pre-arrival, arbitrary and outside observer＇s observation epochs. The analysis of actual waiting-time distribution and some performance measures are carried out. We present some numerical results and discuss special cases of the model.
