Optimal Allocation of Vaccine and Antiviral Drugs for Influenza Containment over Delayed Multiscale Epidemic Model considering Time-Dependent Transmission Rate

In this study, two types of epidemiological models called “within host” and “between hosts” have been studied. The within-host model represents the innate immune response, and the between-hosts model signifies the SEIR (susceptible, exposed, infected, and recovered) epidemic model. The major contribution of this paper is to break the chain of infectious disease transmission by reducing the number of susceptible and infected people via transferring them to the recovered people group with vaccination and antiviral treatment, respectively. Both transfers are considered with time delay. In the first step, optimal control theory is applied to calculate the optimal final time to control the disease within a host’s body with a cost function. To this end, the vaccination that represents the effort that converts healthy cells into resistant-to-infection cells in the susceptible individual’s body is used as the first control input to vaccinate the susceptible individual against the disease. Moreover, the next control input (antiviral treatment) is applied to eradicate the concentrations of the virus and convert healthy cells into resistant-to-infection cells simultaneously in the infected person’s body to treat the infected individual. The calculated optimal time in the first step is considered as the delay of vaccination and antiviral treatment in the SEIR dynamic model. Using Pontryagin’s maximum principle in the second step, an optimal control strategy is also applied to an SEIR mathematical model with a nonlinear transmission rate and time delay, which is computed as optimal time in the first step. Numerical results are consistent with the analytical ones and corroborate our theoretical results.

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Optimal Control of SEIR Epidemic Model Considering Nonlinear Transmission Rate and Time Delay

2021 7th International Conference on Control, Instrumentation and Automation (ICCIA) ◽

10.1109/iccia52082.2021.9403558 ◽

2021 ◽

Author(s):

Zohreh Abbasi ◽

Iman Zamani ◽

Amir Hossein Amiri Mehra ◽

Mohsen Shafieirad

Keyword(s):

Optimal Control ◽

Time Delay ◽

Epidemic Model ◽

Transmission Rate ◽

Nonlinear Transmission

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Optimizing the spatio-temporal allocation of COVID-19 vaccines: Italy as a case study

10.1101/2021.05.06.21256732 ◽

2021 ◽

Author(s):

Joseph Chadi Lemaitre ◽

Damiano Pasetto ◽

Mario Zanon ◽

Enrico Bertuzzo ◽

Lorenzo Mari ◽

...

Keyword(s):

Optimal Control ◽

Disease Transmission ◽

Population Distribution ◽

Transmission Rate ◽

Supply And Distribution ◽

Simple Alternative ◽

Spatio Temporal ◽

Vaccine Distribution ◽

Vaccination Campaigns ◽

Allocation Strategies

While SARS-CoV-2 vaccine distribution campaigns are underway across the world, communities face the challenge of a fair and effective distribution of limited supplies. We wonder whether suitable spatial allocation strategies might significantly improve a campaign's efficacy in averting damaging outcomes. To that end, we address the problem of optimal control of COVID-19 vaccinations in a country-wide geographic and epidemiological context characterized by strong spatial heterogeneities in transmission rate and disease history. We seek the vaccine allocation strategies in space and time that minimize the number of infections in a prescribed time horizon. We examine scenarios of unfolding disease transmission across the 107 provinces of Italy, from January to April 2021, generated by a spatially explicit compartmental COVID-19 model tailored to the Italian geographic and epidemiological context. We develop a novel optimal control framework to derive optimal vaccination strategies given the epidemiological projections and constraints on vaccine supply and distribution logistic. Optimal schemes significantly outperform simple alternative allocation strategies based on incidence, population distribution, or prevalence of susceptibles in each province. Our results suggest that the complex interplay between the mobility network and the spatial heterogeneities imply highly non-trivial prioritization of local vaccination campaigns. The extent of the overall improvements in the objectives grants further inquiry aimed at refining other possibly relevant factors so far neglected. Our work thus provides a proof-of-concept of the potential of optimal control for complex and heterogeneous epidemiological contexts at country, and possibly global, scales.

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Fractional-Order Optimal Control of Fractional-Order Linear Vibration Systems with Time Delay

International Journal of System Dynamics Applications ◽

10.4018/ijsda.2018070104 ◽

2018 ◽

Vol 7 (3) ◽

pp. 72-93

Author(s):

Saeed Balochian ◽

Nahid Rajaee

Keyword(s):

Optimal Control ◽

Time Delay ◽

Fractional Order ◽

Control Method ◽

Linear Structure ◽

Control Input ◽

Linear Vibration ◽

Order Linear ◽

Input Control ◽

Delayed System

Vibration control of fractional-order linear systems in the presence of time delays has been dealt in this article. Considering a delayed n-degree-of freedom linear structure that is modeled by fractional order equations, a fractional-order optimal control is provided to minimize both control input and output of delayed system via quadratic objective function. To do this, first the fractional order model of system that is subject to time delay is rewritten into a non-delay form through a particular transformation. Then, a fractional order optimal controller is provided using the classical optimal control theory to find an optimal input control. A delayed viscose system is then presented as a practical worked-out example. Numerical simulation results are given to confirm the efficiency of the proposed control method.

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An epidemic model for non-first-order transmission kinetics

PLoS ONE ◽

10.1371/journal.pone.0247512 ◽

2021 ◽

Vol 16 (3) ◽

pp. e0247512

Author(s):

Eun-Young Mun ◽

Feng Geng

Keyword(s):

Epidemic Model ◽

Disease Transmission ◽

Transmission Rate ◽

Early Stage ◽

Compartmental Models ◽

Control Measures ◽

Chemical Reaction Kinetics ◽

Rate Law ◽

First Order ◽

First Order Kinetics

Compartmental models in epidemiology characterize the spread of an infectious disease by formulating ordinary differential equations to quantify the rate of disease progression through subpopulations defined by the Susceptible-Infectious-Removed (SIR) scheme. The classic rate law central to the SIR compartmental models assumes that the rate of transmission is first order regarding the infectious agent. The current study demonstrates that this assumption does not always hold and provides a theoretical rationale for a more general rate law, inspired by mixed-order chemical reaction kinetics, leading to a modified mathematical model for non-first-order kinetics. Using observed data from 127 countries during the initial phase of the COVID-19 pandemic, we demonstrated that the modified epidemic model is more realistic than the classic, first-order-kinetics based model. We discuss two coefficients associated with the modified epidemic model: transmission rate constant k and transmission reaction order n. While k finds utility in evaluating the effectiveness of control measures due to its responsiveness to external factors, n is more closely related to the intrinsic properties of the epidemic agent, including reproductive ability. The rate law for the modified compartmental SIR model is generally applicable to mixed-kinetics disease transmission with heterogeneous transmission mechanisms. By analyzing early-stage epidemic data, this modified epidemic model may be instrumental in providing timely insight into a new epidemic and developing control measures at the beginning of an outbreak.

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Analysis of a fuzzy epidemic model with saturated treatment and disease transmission

International Journal of Biomathematics ◽

10.1142/s179352451850002x ◽

2018 ◽

Vol 11 (01) ◽

pp. 1850002 ◽

Cited By ~ 3

Author(s):

Swapan Kumar Nandi ◽

Soovoojeet Jana ◽

Manotosh Manadal ◽

T. K. Kar

Keyword(s):

Epidemic Model ◽

Disease Transmission ◽

Fuzzy Numbers ◽

Transmission Rate ◽

Dynamical Behavior ◽

Threshold Condition ◽

Sis Epidemic Model ◽

Fuzzy Expected Value ◽

Treatment Function ◽

Saturated Treatment

In this paper, we describe an SIS epidemic model where both the disease transmission rate and treatment function are considered in saturated forms. The dynamical behavior of the system is analyzed. The system is customized by considering the disease transmission rate and treatment control as fuzzy numbers and then fuzzy expected value of the infected individuals is determined. The fuzzy basic reproduction number is investigated and a threshold condition of pathogen is derived at which the system undergoes a backward bifurcation.

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Dynamical Behavior of an Epidemic Model in a Fuzzy Transmission

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488515500282 ◽

2015 ◽

Vol 23 (05) ◽

pp. 651-665 ◽

Cited By ~ 6

Author(s):

Prasanta Kumar Mondal ◽

Soovoojeet Jana ◽

Palash Haldar ◽

T. K. Kar

Keyword(s):

Epidemic Model ◽

Disease Transmission ◽

Fuzzy Numbers ◽

Reproduction Number ◽

Transmission Rate ◽

Dynamical Behavior ◽

Threshold Condition ◽

Treatment Control ◽

Fuzzy Expected Value ◽

Treatment Function

In this paper, we have formulated a simple SIS type epidemic model in the presence of treatment control, and we have discussed the dynamical behavior of the system. The system is modified by considering both the disease transmission rate and the treatment function as fuzzy numbers, and also the fuzzy expected value of the infected individuals is calculated. Furthermore, the fuzzy basic reproduction number is investigated and a threshold condition of pathogen is obtained at which the system undergoes a transcritical bifurcation.

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