Estimation and optimal control of the multi-scale dynamics of the Covid-19

Abstract This work aims at a better understanding and the optimal control of the spread of the new severe acute respiratory corona virus 2 (SARS-CoV-2). We first propose a multi-scale model giving insights on the virus population dynamics, the transmission process and the infection mechanism. We consider 10 compartments in the human population in order to take into accounts the effects of different specific mitigation policies. The population of viruses is also partitioned into 10 compartments corresponding respectively to each of the first nine human population compartments and the free viruses available in the environment. We show the global stability of the disease free equilibrium if a given threshold T_0 is less or equal to 1 and we provide how to compute the basic reproduction number R_0. A convergence index T_1 is also defined in order to estimate the speed at which the disease extincts and an upper bound to the time of extinction is given. The existence of the endemic equilibrium is conditional and its description is provided. We evaluate the sensitivity of R_0, T_0 and T_1 to control parameters such as the maximal human density allowed per unit of surface, the rate of disinfection both for people and environment, the mobility probability, the wearing mask probability or efficiency, and the human to human contact rate which results from the previous one. Except the maximal human density allowed per unit of surface, all those parameters have significant effects on the qualitative dynamics of the disease. The most significant is the probability of wearing mask followed by the probability of mobility and the disinfection rate. According to a functional cost taking into consideration economic impacts of SARS-CoV-2, we determine and discuss optimal fighting strategies. The study is applied to real available data from Cameroon and an estimation of model parameters is done. After several simulations, social distancing and the disinfection frequency appear as the main elements of the optimal control strategy.

Download Full-text

Estimation and optimal control of the multi-scale dynamics of the Covid-19

10.1101/2021.03.04.21252880 ◽

2021 ◽

Author(s):

David Jaurès Fotsa-Mbogne ◽

Stéphane Yanick Tchoumi ◽

Yannick Kouakep-Tchaptchie ◽

Vivient Corneille Kamla ◽

Jean-Claude Kamgang ◽

...

Keyword(s):

Optimal Control ◽

Human Population ◽

Virus Transmission ◽

Scale Model ◽

Model Parameters ◽

Optimal Control Strategy ◽

Or Efficiency ◽

Human Virus ◽

Multi Scale ◽

Human Density

AbstractThis work aims at a better understanding and the optimal control of the spread of the new severe acute respiratory corona virus 2 (SARS-CoV-2). We first propose a multi-scale model giving insights on the virus population dynamics, the transmission process and the infection mechanism. We consider 10 compartments in the human population in order to take into accounts the effects of different specific mitigation policies: susceptible, infected, infectious, quarantined, hospitalized, treated, recovered, non-infectious dead, infectious dead, buried. The population of viruses is also partitioned into 10 compartments corresponding respectively to each of the first nine human population compartments and the free viruses available in the environment. Indeed, we have human to human virus transmission, human to environment virus transmission, environment to human virus transmission and self infection by susceptible individuals. We show the global stability of the disease free equilibrium if a given threshold 𝒯0 is less or equal to 1 and we provide how to compute the basic reproduction number ℛ0. A convergence index 𝒯1 is also defined in order to estimate the speed at which the disease extincts and an upper bound to the time of extinction is given. The existence of the endemic equilibrium is conditional and its description is provided. We evaluate the sensitivity of ℛ0, 𝒯0 and 𝒯1 to control parameters such as the maximal human density allowed per unit of surface, the rate of disinfection both for people and environment, the mobility probability, the wearing mask probability or efficiency, and the human to human contact rate which results from the previous one. Except the maximal human density allowed per unit of surface, all those parameters have significant effects on the qualitative dynamics of the disease. The most significant is the probability of wearing mask followed by the probability of mobility and the disinfection rate. According to a functional cost taking into consideration economic impacts of SARS-CoV-2, we determine and discuss optimal fighting strategies. The study is applied to real available data from Cameroon and an estimation of model parameters is done. After several simulations, social distancing and the disinfection frequency appear as the main elements of the optimal control strategy.

Download Full-text

Estimation and Optimal Control of the Multiscale Dynamics of Covid-19: A Case Study From Cameroon

10.21203/rs.3.rs-674622/v1 ◽

2021 ◽

Author(s):

David Jaures FOTSA MBOGNE ◽

Stéphane Yanick TCHOUMI ◽

Yannick KOUAKEP TCHAPTCHIE ◽

Vivient Corneille KAMLA ◽

Jean Claude KAMGANG ◽

...

Keyword(s):

Optimal Control ◽

Human Population ◽

Scale Model ◽

Or Efficiency ◽

Multi Scale ◽

Human Contact ◽

Multiscale Dynamics ◽

Disease Free ◽

Human Density

Download Full-text

Modeling the Impact of Optimal Control Strategies on the Dynamics of Zika Virus Disease Using the Sterile Insect Technology

Journal of Advances in Mathematics and Computer Science ◽

10.9734/jamcs/2020/v35i830310 ◽

2020 ◽

pp. 13-33

Author(s):

Atokolo William ◽

Akpa Johnson ◽

Daniel Musa Alih ◽

Olayemi Kehinde Samuel ◽

C. E. Mbah Godwin

Keyword(s):

Optimal Control ◽

Control Strategy ◽

Zika Virus ◽

Human Population ◽

Necessary Conditions ◽

Virus Disease ◽

Control Strategies ◽

Control Measures ◽

Optimal Control Strategy ◽

The Impact

This work is aimed at formulating a mathematical model for the control of zika virus infection using Sterile Insect Technology (SIT). The model is extended to incorporate optimal control strategy by introducing three control measures. The optimal control is aimed at minimizing the number of Exposed human, Infected human and the total number of Mosquitoes in a population and as such reducing contacts between mosquitoes and human, human to human and above all, eliminates the population of Mosquitoes. The Pontryagin’s maximum principle was used to obtain the necessary conditions, find the optimality system of our model and to obtain solution to the control problem. Numerical simulations result shows that; reduction in the number of Exposed human population, Infected human population and reduction in the entire population of Mosquito population is best achieved using the optimal control strategy.

Download Full-text

Data Assimilation in a Multi-Scale Model

Mathematics of Climate and Weather Forecasting ◽

10.1515/mcwf-2017-0006 ◽

2017 ◽

Vol 3 (1) ◽

Author(s):

Guannan Hu ◽

Christian L. E. Franzke

Keyword(s):

Data Assimilation ◽

Autoregressive Process ◽

Scale Model ◽

Prototype Model ◽

Model Parameters ◽

Model Errors ◽

Multi Scale ◽

Parameterization Schemes ◽

Scale Models ◽

Lorenz 96

AbstractData assimilation for multi-scale models is an important contemporary research topic. Especially the role of unresolved scales and model error in data assimilation needs to be systematically addressed. Here we examine these issues using the Ensemble Kalman filter (EnKF) with the two-level Lorenz-96 model as a conceptual prototype model of the multi-scale climate system. We use stochastic parameterization schemes to mitigate the model errors from the unresolved scales. Our results indicate that a third-order autoregressive process performs better than a first-order autoregressive process in the stochastic parameterization schemes, especially for the system with a large time-scale separation.Model errors can also arise from imprecise model parameters. We find that the accuracy of the analysis (an optimal estimate of a model state) is linearly correlated to the forcing error in the Lorenz-96 model. Furthermore, we propose novel observation strategies to deal with the fact that the dimension of the observations is much smaller than the model states. We also propose a new analog method to increase the size of the ensemble when its size is too small.

Download Full-text

Mathematical Modelling of Listeriosis Epidemics in Animal and Human Population with Optimal Control.

Tamkang Journal of Mathematics ◽

10.5556/j.tkjm.51.2020.2860 ◽

2020 ◽

Vol 51 (4) ◽

pp. 261-287

Author(s):

Shaibu Osman ◽

Oluwole Daniel Makinde ◽

David Mwangi Theuri

Keyword(s):

Optimal Control ◽

Human Population ◽

Model Problem ◽

Control Strategies ◽

Model Parameters ◽

Contaminated Food ◽

Serious Disease ◽

The Stability ◽

The Impact ◽

Disease Free

Listeriosis is a serious disease caused by the germ Listeria monocytogenes. People usually become ill with listeriosis after eating contaminated food including meat. The disease primarily affects pregnant women, newborns, older adults, and people with weakened immune systems. In this paper, we propose and scrutinize a model problem describing the transmission dynamics of Listeriosis epidemic in animal and human population using the stability theory of differential equations. The model is qualitatively analysed for the basic reproduction number as well as possibility of forward and backward bifurcation with respect to the stability of disease free and endemic equilibria. The impact of the model parameters on the disease was evaluated via sensitivity analysis. An extension of the model to include time dependent control variables such as treatment, vaccination and education of susceptible (human) is carried out. Using Pontryagin’s Maximum Principle, we obtain the optimal control strategies needed for combating Listeriosis disease. Numerical simulation of the model is performed and pertinent results are displayed graphically and discussed quantitatively.

Download Full-text

A Mathematical Model for Coinfection of Listeriosis and Anthrax Diseases

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/2018/1725671 ◽

2018 ◽

Vol 2018 ◽

pp. 1-14 ◽

Cited By ~ 2

Author(s):

Shaibu Osman ◽

Oluwole Daniel Makinde

Keyword(s):

Human Population ◽

Reproduction Number ◽

Zoonotic Diseases ◽

Transmission Dynamics ◽

Model Parameters ◽

Contact Rate ◽

Disease Dynamics ◽

Human Contact ◽

The Stability ◽

Disease Free

Listeriosis and Anthrax are fatal zoonotic diseases caused by Listeria monocytogene and Bacillus Anthracis, respectively. In this paper, we proposed and analysed a compartmental Listeriosis-Anthrax coinfection model describing the transmission dynamics of Listeriosis and Anthrax epidemic in human population using the stability theory of differential equations. Our model revealed that the disease-free equilibrium of the Anthrax model only is locally stable when the basic reproduction number is less than one. Sensitivity analysis was carried out on the model parameters in order to determine their impact on the disease dynamics. Numerical simulation of the coinfection model was carried out and the results are displayed graphically and discussed. We simulate the Listeriosis-Anthrax coinfection model by varying the human contact rate to see its effects on infected Anthrax population, infected Listeriosis population, and Listeriosis-Anthrax coinfected population.

Download Full-text

A Modified Optimal Control Strategy for a Five-Finger Robotic Hand

International Journal of Robotics and Automation Technology ◽

10.15377/2409-9694.2014.01.01.1 ◽

2014 ◽

Vol 1 (1) ◽

pp. 3-10 ◽

Cited By ~ 4

Author(s):

Cheng-Hung Chen ◽

◽

D. Naidu

Keyword(s):

Optimal Control ◽

Control Strategy ◽

Robotic Hand ◽

Optimal Control Strategy

Download Full-text

Three-dimensional Reconstruction of Microscopic Image Based on Multi-ST Algorithm

Journal of Imaging Science and Technology ◽

10.2352/j.imagingsci.technol.2020.64.2.020506 ◽

2020 ◽

Vol 64 (2) ◽

pp. 20506-1-20506-7

Author(s):

Min Zhu ◽

Rongfu Zhang ◽

Pei Ma ◽

Xuedian Zhang ◽

Qi Guo

Keyword(s):

3D Reconstruction ◽

Three Dimensional ◽

Scale Model ◽

Microscopic Image ◽

Multi Scale ◽

Gaussian Pyramid ◽

Cost Aggregation ◽

Dimensional Reconstruction ◽

Image Pairs ◽

Accurate Matching

Abstract Three-dimensional (3D) reconstruction is extensively used in microscopic applications. Reducing excessive error points and achieving accurate matching of weak texture regions have been the classical challenges for 3D microscopic vision. A Multi-ST algorithm was proposed to improve matching accuracy. The process is performed in two main stages: scaled microscopic images and regularized cost aggregation. First, microscopic image pairs with different scales were extracted according to the Gaussian pyramid criterion. Second, a novel cost aggregation approach based on the regularized multi-scale model was implemented into all scales to obtain the final cost. To evaluate the performances of the proposed Multi-ST algorithm and compare different algorithms, seven groups of images from the Middlebury dataset and four groups of experimental images obtained by a binocular microscopic system were analyzed. Disparity maps and reconstruction maps generated by the proposed approach contained more information and fewer outliers or artifacts. Furthermore, 3D reconstruction of the plug gauges using the Multi-ST algorithm showed that the error was less than 0.025 mm.

Download Full-text