scholarly journals Deterministic Epidemic Models for Ebola Infection with Time-Dependent Controls

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Eric Okyere ◽  
Johnson De-Graft Ankamah ◽  
Anthony Kodzo Hunkpe ◽  
Dorcas Mensah
Keyword(s):  
Optimal Control ◽  
Disease Transmission ◽  
Ebola Virus ◽  
Virus Disease ◽  
Control Strategies ◽  
Hamiltonian Function ◽  
Epidemic Models ◽  
Adjoint Equations ◽  
Time Dependent ◽  
Control Analysis

In this paper, we have studied epidemiological models for Ebola infection using nonlinear ordinary differential equations and optimal control theory. We considered optimal control analysis of SIR and SEIR models for the deadly Ebola infection using vaccination, treatment, and educational campaign as time-dependent control functions. We have applied indirect methods to study existing deterministic optimal control epidemic models for Ebola virus disease. These methods in optimal control are based on Hamiltonian function and Pontryagin’s maximum principle to construct adjoint equations and optimality systems. The forward-backward sweep numerical scheme with the fourth-order Runge–Kutta method is used to solve the optimality system for the various control strategies. From our numerical illustrations, we can conclude that effective educational campaigns and vaccination of susceptible individuals as well as effective treatments of infected individuals can help reduce the disease transmission.

scholarly journals Controlling the Spread of COVID-19: Optimal Control Analysis

2020 ◽  
Author(s):  
Chinwendu E. Madubueze ◽  
Sambo Dachollom ◽  
Isaac Obiajulu Onwubuya
Keyword(s):  
Optimal Control ◽  
Control Strategies ◽  
Public Health Education ◽  
Time Dependent ◽  
World Health ◽  
Critical Parameters ◽  
Control Analysis ◽  
Invariant Region ◽  
Control Approach ◽  
Health Organization

AbstractCoronavirus disease 2019 (COVID-19) is a disease caused by Severe acute respiratory syndrome coronavirus 2 (SARS CoV-2). It was declared on March 11, 2020, by the World Health Organization as pandemic disease. The disease has neither approved medicine nor vaccine and has made government and scholars search for drastic measures in combating the pandemic. Regrettably, the spread of the virus and mortality due to COVID-19 has continued to increase daily. Hence, it is imperative to control the spread of the disease particularly using non-pharmacological strategies such as quarantine, isolation and public health education. This work studied the effect of these different control strategies as time-dependent interventions using mathematical modeling and optimal control approach to ascertain their contributions in the dynamic transmission of COVID-19. The model was proven to have an invariant region and was well-posed. The basic reproduction number was computed with and without interventions and was used to carry out the sensitivity analysis that identified the critical parameters contributing to the spread of COVID-19. The optimal control analysis was carried out using the Pontryagin’s maximum principle to figure out the optimal strategy necessary to curtail the disease. The findings of the optimal control analysis and numerical simulations revealed that time-dependent interventions reduced the number of exposed and infected individuals compared to time-independent interventions. These interventions were time-bound and best implemented within the first 100 days of the outbreak. Again, the combined implementation of only two of these interventions produced a good result in reducing infection in the population, while the combined implementation of all three interventions performed better, even though zero infection was not achieved in the population. This implied that multiple interventions need to be deployed early in order to the virus to the barest minimum.

scholarly journals Controlling the Spread of COVID-19: Optimal Control Analysis

2020 ◽  
Vol 2020 ◽  
pp. 1-14 ◽  
Author(s):  
Chinwendu E. Madubueze ◽  
Sambo Dachollom ◽  
Isaac Obiajulu Onwubuya
Keyword(s):  
Optimal Control ◽  
Control Strategies ◽  
Public Health Education ◽  
Time Dependent ◽  
World Health ◽  
Critical Parameters ◽  
Control Analysis ◽  
Invariant Region ◽  
Control Approach ◽  
Health Organization

Coronavirus disease 2019 (COVID-19) is a disease caused by severe acute respiratory syndrome coronavirus 2 (SARS CoV-2). It was declared on March 11, 2020, by the World Health Organization as pandemic disease. The disease has neither approved medicine nor vaccine and has made governments and scholars search for drastic measures in combating the pandemic. Regrettably, the spread of the virus and mortality due to COVID-19 has continued to increase daily. Hence, it is imperative to control the spread of the disease particularly using nonpharmacological strategies such as quarantine, isolation, and public health education. This work studied the effect of these different control strategies as time-dependent interventions using mathematical modeling and optimal control approach to ascertain their contributions in the dynamic transmission of COVID-19. The model was proven to have an invariant region and was well-posed. The basic reproduction number and effective reproduction numbers were computed with and without interventions, respectively, and were used to carry out the sensitivity analysis that identified the critical parameters contributing to the spread of COVID-19. The optimal control analysis was carried out using the Pontryagin’s maximum principle to figure out the optimal strategy necessary to curtail the disease. The findings of the optimal control analysis and numerical simulations revealed that time-dependent interventions reduced the number of exposed and infected individuals compared to time-independent interventions. These interventions were time-bound and best implemented within the first 100 days of the outbreak. Again, the combined implementation of only two of these interventions produced a good result in reducing infection in the population. While, the combined implementation of all three interventions performed better, even though zero infection was not achieved in the population. This implied that multiple interventions need to be deployed early in order to reduce the virus to the barest minimum.

AN OPTIMAL CONTROL MODEL FOR EBOLA VIRUS DISEASE

2016 ◽  
Vol 24 (01) ◽  
pp. 29-49 ◽  
Author(s):  
SYLVIE DIANE DJIOMBA NJANKOU ◽  
FARAI NYABADZA
Keyword(s):  
Optimal Control ◽  
Ebola Virus ◽  
Virus Disease ◽  
Control Strategies ◽  
Sufficient Conditions ◽  
Case Fatality ◽  
Ebola Virus Disease ◽  
Joint Control ◽  
Transversality Conditions ◽  
Necessary And Sufficient

The most deadly Ebola outbreak in the history, which started in December [Formula: see text], is currently under control. The high case fatality rate of the Ebola outbreak inspired local and international control strategies. In this paper, the dynamics of Ebola virus disease is modeled in the presence of three control strategies. The model describes the evolution of the disease in the population when educational campaigns, active case-finding and pharmaceutical interventions are implemented as control strategies against the disease. We prove the existence of an optimal control set and analyze the necessary and sufficient conditions, optimality and transversality conditions. We conclude through numerical simulations that containing an Ebola outbreak needs early and long-term implementation of joint control strategies.

Spatial-temporal transmission dynamics and control of infectious diseases: Ebola virus disease (EVD) as a case study

2018 ◽  
Author(s):  
Cécile Viboud ◽  
Hélène Broutin ◽  
Gerardo Chowell
Keyword(s):  
Infectious Diseases ◽  
Disease Transmission ◽  
Ebola Virus ◽  
Temporal Dynamics ◽  
Virus Disease ◽  
Spatial Dynamics ◽  
Childhood Diseases ◽  
Middle Income ◽  
Theoretical Concepts ◽  
Dynamics And Control

Disentangling the spatial-temporal dynamics of infectious disease transmission is important to address issues of disease persistence, epidemic growth and optimal control. In this chapter, we review key concepts relating to the spatial-temporal dynamics of infectious diseases in meta-populations, whereby geographically separate subpopulations are connected by migration or mobility rates. We review the dynamics of colonization, persistence and extinction of emerging and recurrent pathogens in meta-populations; the role of demographic and environmental factors; and geographic heterogeneity in epidemic growth rate. We illustrate theoretical concepts by reviewing the spatial dynamics of childhood diseases and other acute infections in low- and middle-income countries, and provide a detailed description of the spatial-temporal dynamics of the 2014–16 Ebola epidemic in West Africa. We further discuss how increased availability of empirical data and recent methodological developments provide a deeper mechanistic understanding of transmission processes in space and time, and make recommendations for future work.

scholarly journals Global Stability and Optimal Control of Dengue with Two Coexisting Virus Serotypes

MATEMATIKA ◽  
2019 ◽  
Vol 35 (4) ◽  
pp. 149-170
Author(s):  
Afeez Abidemi ◽  
Rohanin Ahmad ◽  
Nur Arina Bazilah Aziz
Keyword(s):  
Optimal Control ◽  
Global Stability ◽  
Disease Transmission ◽  
Deterministic Model ◽  
Control Strategies ◽  
Equilibrium Points ◽  
Effective Control ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Boundary Equilibrium

This study presents a two-strain deterministic model which incorporates Dengvaxia vaccine and insecticide (adulticide) control strategies to forecast the dynamics of transmission and control of dengue in Madeira Island if there is a new outbreak with a different virus serotypes after the first outbreak in 2012. We construct suitable Lyapunov functions to investigate the global stability of the disease-free and boundary equilibrium points. Qualitative analysis of the model which incorporates time-varying controls with the specific goal of minimizing dengue disease transmission and the costs related to the control implementation by employing the optimal control theory is carried out. Three strategies, namely the use of Dengvaxia vaccine only, application of adulticide only, and the combination of Dengvaxia vaccine and adulticide are considered for the controls implementation. The necessary conditions are derived for the optimal control of dengue. We examine the impacts of the control strategies on the dynamics of infected humans and mosquito population by simulating the optimality system. The disease-freeequilibrium is found to be globally asymptotically stable whenever the basic reproduction numbers associated with virus serotypes 1 and j (j 2 {2, 3, 4}), respectively, satisfy R01,R0j 1, and the boundary equilibrium is globally asymptotically stable when the related R0i (i = 1, j) is above one. It is shown that the strategy based on the combination of Dengvaxia vaccine and adulticide helps in an effective control of dengue spread in the Island.

A multi-delay model for pest control with awareness induced interventions — Hopf bifurcation and optimal control analysis

2020 ◽  
Vol 13 (06) ◽  
pp. 2050047
Author(s):  
Fahad Al Basir
Keyword(s):  
Optimal Control ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Time Delays ◽  
Control Strategies ◽  
Control Analysis ◽  
Agricultural Practice ◽  
Delay Model ◽  
Awareness Campaigns ◽  
Farming Awareness

Farming awareness is an important measure for pest controlling in agricultural practice. Time delay in controlling pest may affect the system. Time delay occurs in organizing awareness campaigns, also time delay may takes place in becoming aware of the control strategies or implementing suitable controlling methods informed through social media. Thus we have derived a mathematical model incorporating two time delays into the system and Holling type-II functional response. The existence and the stability criteria of the equilibria are obtained in terms of the basic reproduction number and time delays. Stability changes occur through Hopf-bifurcation when time delays cross the critical values. Optimal control theory has been applied for cost-effectiveness of the delayed system. Numerical simulations are carried out to justify the analytical results. This study shows that optimal farming awareness through radio, TV etc. can control the delay induced bifurcation in a cost-effective way.

Sign in / Sign up

Export Citation Format

Share Document