scholarly journals Analysis and Optimal Control Intervention Strategies of a Waterborne Disease Model: A Realistic Case Study

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Obiora Cornelius Collins ◽  
Kevin Jan Duffy
Keyword(s):  
Optimal Control ◽  
Disease Transmission ◽  
Disease Model ◽  
Minimum Cost ◽  
Intervention Strategies ◽  
Cholera Outbreak ◽  
Waterborne Disease ◽  
Control Intervention ◽  
Mathematical Analyses

A mathematical model is formulated that captures the essential dynamics of waterborne disease transmission under the assumption of a homogeneously mixed population. The important mathematical features of the model are determined and analysed. The model is extended by introducing control intervention strategies such as vaccination, treatment, and water purification. Mathematical analyses of the control model are used to determine the possible benefits of these control intervention strategies. Optimal control theory is utilized to determine how to reduce the spread of a disease with minimum cost. The model is validated using a cholera outbreak in Haiti.

scholarly journals Dynamical System Analysis and Optimal Control Measures of Lassa Fever Disease Model

2020 ◽  
Vol 2020 ◽  
pp. 1-18 ◽  
Author(s):  
Ifeanyi Sunday Onah ◽  
Obiora Cornelius Collins ◽  
Praise-God Uchechukwu Madueme ◽  
Godwin Christopher Ezike Mbah
Keyword(s):  
Optimal Control ◽  
Disease Transmission ◽  
System Analysis ◽  
Disease Model ◽  
Minimum Cost ◽  
Lassa Fever ◽  
Control Measures ◽  
Extended Model ◽  
Lassa Virus ◽  
Intervention Measures

Lassa fever is an animal-borne acute viral illness caused by the Lassa virus. This disease is endemic in parts of West Africa including Benin, Ghana, Guinea, Liberia, Mali, Sierra Leone, and Nigeria. We formulate a mathematical model for Lassa fever disease transmission under the assumption of a homogeneously mixed population. We highlighted the basic factors influencing the transmission of Lassa fever and also determined and analyzed the important mathematical features of the model. We extended the model by introducing various control intervention measures, like external protection, isolation, treatment, and rodent control. The extended model was analyzed and compared with the basic model by appropriate qualitative analysis and numerical simulation approach. We invoked the optimal control theory so as to determine how to reduce the spread of the disease with minimum cost.

scholarly journals Optimal Control of Aquatic Diseases: A Case Study of Yemen’s Cholera Outbreak

2020 ◽  
Vol 185 (3) ◽  
pp. 1008-1030 ◽  
Author(s):  
Ana P. Lemos-Paião ◽  
Cristiana J. Silva ◽  
Delfim F. M. Torres ◽  
Ezio Venturino
Keyword(s):  
Optimal Control ◽  
Cholera Outbreak

Optimal control of intervention strategies in malaria–tuberculosis co-infection with relapse

2018 ◽  
Vol 11 (02) ◽  
pp. 1850017 ◽  
Author(s):  
Peter Mpasho Mwamtobe ◽  
Simphiwe Mpumelelo Simelane ◽  
Shirley Abelman ◽  
Jean Michel Tchuenche
Keyword(s):  
Optimal Control ◽  
Sensitivity Analysis ◽  
Stable Disease ◽  
Disease Transmission ◽  
Backward Bifurcation ◽  
Intervention Strategies ◽  
Relative Importance ◽  
Disease Dynamics ◽  
Epidemiological Features ◽  
Disease Free

A model which incorporates some of the basic epidemiological features of the co-dynamics of malaria and tuberculosis (TB) is formulated and the effectiveness of current intervention strategies of these two diseases is analyzed. The malaria-only and TB-only models are considered first. Global stability disease-free steady states of the two sub-models does not hold due to the co-existence of stable disease-free with stable endemic equilibria, a phenomenon known as backward bifurcation. The dynamics of the dual malaria–TB model with intervention strategies are also analyzed. Numerical simulations of the malaria–TB model are carried out to determine whether the two diseases can co-exist. Lastly, sensitivity analysis on key parameters that drive the disease dynamics is performed in order to identify their relative importance to disease transmission.

scholarly journals Transmission dynamics model of Tuberculosis with optimal control strategies in Haramaya district, Ethiopia

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Doyo Kereyu ◽  
Seleshi Demie
Keyword(s):  
Optimal Control ◽  
Disease Transmission ◽  
Reproduction Number ◽  
Control Strategies ◽  
Minimum Cost ◽  
Optimal Level ◽  
Qualitative Behavior ◽  
Dynamics Model ◽  
Haramaya District ◽  
Disease Free

AbstractIn this study, we use a compartmental nonlinear deterministic mathematical model to investigate the effect of different optimal control strategies in controlling Tuberculosis (TB) disease transmission in the community. We employ stability theory of differential equations to investigate the qualitative behavior of the model by obtaining the basic reproduction number and determining the local stability conditions for the disease-free and endemic equilibria. We consider three control strategies representing distancing, case finding, and treatment efforts and numerically compare the levels of exposed and infectious populations with and without control strategies. The results suggest that combination of all controls is the best strategy to eradicate TB disease from the community at an optimal level with minimum cost of interventions.

scholarly journals Mathematical modeling and optimal intervention strategies of the COVID-19 outbreak

2021 ◽  
Author(s):  
Jayanta Mondal ◽  
Subhas Khajanchi
Keyword(s):  
Optimal Control ◽  
Basic Reproduction Number ◽  
Disease Transmission ◽  
Numerical Solutions ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Intervention Strategy ◽  
Intervention Strategies ◽  
Qualitative Behavior ◽  
The Basic Reproduction Number

Abstract 32,737,939 active cases and 438,210 deaths because of COVID-19 pandemic were recorded on 30 August 2021 in India. To end this ongoing global COVID-19 pandemic, there is an urgent need to implement multiple population-wide policies like social distancing, testing more people and contact tracing. To predict the course of the pandemic and come up with a strategy to control it effectively, a compartmental model has been established. The following six stages of infection are taken into consideration: susceptible ($S$), asymptomatic infected ($A$), clinically ill or symptomatic infected ($I$), quarantine ($Q$), isolation ($J$) and recovered ($R$), collectively termed as SAIQJR. The qualitative behavior of the model and the stability of biologically realistic equilibrium points are investigated in terms of the basic reproduction number. We performed sensitivity analysis with respect to the basic reproduction number and obtained that the disease transmission rate has an impact in mitigating the spread of diseases. Moreover, considering the non-pharmaceutical and pharmaceutical intervention strategies as control functions, an optimal control problem is implemented to mitigate the disease fatality. To reduce the infected individuals and to minimize the cost of the controls, an objective functional has been constructed and solved with the aid of Pontryagin's Maximum Principle. The implementation of optimal control strategy at the start of a pandemic tends to decrease the intensity of epidemic peaks, spreading the maximal impact of an epidemic over an extended time period. Extensive numerical simulations show that the implementation of intervention strategy has an impact in controlling the transmission dynamics of COVID-19 epidemic. Further, our numerical solutions exhibit that the combination of three controls are more influential when compared with the combination of two controls as well as single control. Therefore the implementation of all the three control strategies may help to mitigate novel coronavirus disease transmission at this present epidemic scenario.

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