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

Abstract

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.

Vaccination and isolation based control design of the COVID-19 pandemic based on adaptive neuro fuzzy inference system optimized with the genetic algorithm

“…In the following, the present study is compared to some studies specifically to show the capability of the given controller. Authors in Cooper et al ( 2020 ); Abbasi et al 2021b ) introduced an optimal technique to control the SEIR model for Influenza and COVID-19, respectively. Those papers aimed to reduce the number of susceptible and infected individuals and increase the number of recovered individuals using minimum vaccination and antiviral treatment rates.…”

A Statistical Moment-Based Spectral Approach to the Chance-Constrained Stochastic Optimal Control of Epidemic Models

“…In [14], an optimal control approach is used to analyse the transmission dynamics of HIV/AIDS by combining two control measures, namely standard antiretroviral therapy and AIDS treatments. The optimal allocation of vaccine and antiviral drugs for influenza containment over a time-delayed two-stage epidemic model is studied in [15]. The optimal control problem of a fractional-order delayed epidemic model with a saturated incidence rate and saturated treatment function is studied in [16], in which vaccination and increasing treatment intensity are the control interventions.…”