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A two‐compartmental open model to study metabolism/elimination that arise in clinical observation and pharmacokinetics, is presented. The purpose of this work is to show how it is possible to combine the two methods of Alienor and Adomian with observability identification and controllability principles to optimize drug doses.

Cliniciansa try to know how to detect patients at high risk of 5‐Fu (intravnous administration). The approach is to use a two‐compartmental open model to study its metabolism/elimination and assume that it has a nonlinear behaviour. The methodology chosen brings together two proven techniques to solve the arising differential system. A case study “5‐Fu pharmacokinetics” provides an illustrative application of the combined methods.

On the basis of the numerical results obtained in the case study it was found that a chart could be set up for individual dose adjustment according to individual parameters relating to dose and plasma concentration. The use of mathematical modeling in this field was shown to be justified.

This research is especially important in the pharmaceutical industry since it allows the prediction of drug behaviour in the body. In future work, we will consider the controllability of this problem.

Improved mathematical modelling would allow physicians to treat patients in an optimal way without compromising their comfort or safety. The practitioner would need only to follow a specified procedure.

The new procedure will be especially important to the pharmaceutical industry and this methodology, combined with statistical analysis, will help to improve drug benefits.

Mathematical models have been constructed to aid in the understanding of the pharmacokinetics of different drugs. Gives a mathematical analysis of the courses over time of absorption, distribution and elimination of a drug in a six‐compartment linear mammillary model. A mammillary model is a compartmental model in which a central compartment (the udder of a cow) is related to all other compartments, but there are no relations between the latter. This linear mammillary model can be used to study the kinetics of protein metabolism in the organism. An optimization method (ALIENOR) is used which reduces the unknown parameters involved to a single variable. Thus, the problem requires the global minimum of a function of a single variable. The results obtained with the method described are compared with those obtained with the generalized least‐squares method.

This paper deals with mathematical and numerical methods for defining optimal therapeutics associated with drugs action models. To obtain the optimal control corresponding to some criteria analytical and numerical methods are proposed. An original optimization technique giving the global optimum will be described and used. It is based on a space filling curve idea. A new variant of the dynamic programming method is also proposed, this leads to a simple optimization problem.

This study aims to analyze the epidemic modeling applications and policy‐making strategies for six different infectious diseases in a number of countries, thus comparing and contrasting research in underdeveloped, developing, and developed countries.

A systematic review has been conducted by identifying relevant studies for six diseases from different sources and selecting 74 publications for inclusion. These selected publications are classified and analyzed based on infectious disease, control policies, theme and objective, methodology, origin of population data, publication year and results.

Review results indicate that disaster preparedness and surveillance plans for epidemics are available mostly for developed countries. There is a need for further research in both developing and developed countries because of the ease of dispersion, which constitutes a universal threat. Analysis of the publications suggests that epidemic disasters are mostly studied by researchers in the field of medicine or biology with the aim of assessing the potential impact of an epidemic. The authors highlight the need for further research in operations research and disaster management fields and propose further research directions in the area of disaster management.

This review emphasizes the importance of epidemic disaster modeling for the preparedness stage of disaster management and policy making. Disease and population‐specific intervention policies (e.g. vaccination) reported in this review should set an example and help policy makers during their decision making.

Potential use of the epidemiological modeling on further planning and decision‐making issues in the context of disaster management is studied for the first time.

Several national- and state-level studies have been predicting the course of the COVID-19 pandemic using supervised machine learning algorithms. However, the comparison of such models has not been discussed before. This is the first-ever research wherein the two leading models, susceptible-infected-recovered (SIR) and logistic are compared. The purpose of this study is to observe their utility, at both the National and Municipal Corporation level in India.

The modified SIR and the logistic were deployed for analysis of the COVID-19 patients’ database of India and three Municipal Corporations, namely, Akola, Kalyan-Dombivli and Mira-Bhayander. The data for the study was collected from the official notifications for COVID-19 released by respective government websites.

This study provides evidence to show the superiority of the modified SIR over the logistic model. The models give accurate predictions for a period up to 14 days. The prediction accuracy of the models is limited due to change in government policies. This can be observed by the drastic increase in the COVID-19 cases after Unlock 1.0 in India. The models have proven that they can effectively predict for both National and Municipal Corporation level database.

The modified SIR model can be used to signify the practicality and effectiveness of the decisions taken by the authorities to contain the spread of coronavirus.

This study modifies the SIR model and also identifies and fulfills the need to find a more accurate prediction algorithm to help curb the pandemic.

To prove two results. Namely that if in a linear homogeneous bicompartmental system one compartment is measured then it is indefinable. The second one is related to the identification of non‐linear compartmental models by mean of a linear method.

The first result is generalized to linear non‐homogeneous bicompartmental systems of Michaelis‐Menten (M‐M systems). The second one is related to the identification of a non‐linear compartmental model. The obtained linear system is not homogeneous and must be generalized to nonhomogeneous systems. Then the Jacobian matrix associated to the M‐M systems is identified and the M‐M parameters are deduced by continuity from the Cauchy problem's solution.

Both stated results were proved and any open linear bicompartmental system whether homogeneous or not, of the type I is identifiable.

In compartmental analysis the exchange hypothesis allows us to represent a model of any phenomenon depending on time. Many phenomena require “the enzyme reactions” leading to the M‐M laws. These laws assert that the quantity of matter going from compartment can be defined and M‐M constants prescribed. This research considers both homogeneous and nonhomogeneous systems cases.

Contributes to the identification of linear and non‐linear bicompartmental systems which are of biocybernetical significance.

The two proven results are new and applicable.

This paper studies the existence and uniqueness of parameters identification in linear compartmental systems using successive resolutions of linear algebraic systems. These results can be exploited to build up simple numerical algorithms involving only algebraic linear systems. Compartmental analysis is the main mathematical technique for modelling phenomena arising in biology and medicine.

This paper aims to assess the economic impact of uniform COVID-controlling policies that were implemented by the US government in 2020 and compare it with hypothetical targeted policies that consider the heterogenous effect of COVID-19 on different age groups.

The author began by showing that the adjusted SEQIHR model is a good fit to the US COVID-induced daily death data in that it can capture the nonlinearities of the data very well. Then, he used this model with extra parameters to evaluate the economic effects of COVID-19 through its impact on the job market.

The results show that targeted COVID-controlling policies could reduce the US death rate and GDP loss to 0.03% and 2%, respectively. By comparing these results with uniform COVID-controlling policies, which led to a 0.1% death rate and 3.5% GDP loss, we could conclude that the death rate reduction is 0.07%. Approximately 378,000 Americans died because of COVID-19 during 2020, therefore, reducing the death rate to 0.03% means saving a significant proportion of the COVID-19 casualties, around 280,000 lives.

To the best of the author's knowledge, this paper is the first study to assess the economic impacts of COVID-controlling policies by using the multirisk SEQIHR model.

After the identification of a novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) at Wuhan, China, a pandemic was widely spread worldwide. In Italy, about 240,000 people were infected because of this virus including 34,721 deaths until the end of June 2020. To control this new pandemic, epidemiologists recommend the enforcement of serious mitigation measures like country lockdown, contact tracing or testing, social distancing and self-isolation.

This paper presents the most popular epidemic model of susceptible (S), exposed (E), infected (I) and recovered (R) collectively called SEIR to understand the virus spreading among the Italian population.

Developed SEIR model explains the infection growth across Italy and presents epidemic rates after and before country lockdown. The results demonstrated that follow-up of strict measures such that country lockdown along with high testing is making Italy practically a pandemic-free country.

These models largely help to estimate and understand how an infectious agent spreads in a particular country and how individual factors can affect the dynamics. Further studies like classical SEIR modeling can improve the quality of data and implementation of this modeling could represent a novelty of epidemic models.