Mathematical Analyses on the Effects of Control Measures for a Waterborne Disease Model with Socioeconomic Conditions

2021 ◽  
Vol 28 (1) ◽  
pp. 19-32
Author(s):  
Obiora Cornelius Collins ◽  
Kevin Jan Duffy
Keyword(s):  
Disease Model ◽  
Control Measures ◽  
Socioeconomic Conditions ◽  
Waterborne Disease ◽  
Mathematical Analyses

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.

Analysis of a waterborne disease model with socioeconomic classes

2015 ◽  
Vol 269 ◽  
pp. 86-93 ◽  
Author(s):  
O.C. Collins ◽  
Suzanne L. Robertson ◽  
K.S. Govinder
Keyword(s):  
Disease Model ◽  
Waterborne Disease

scholarly journals Application of Optimal Control to Long Term Dynamics of COVID-19 Disease in South Africa

2020 ◽  
Author(s):  
Farai Nyabadza ◽  
Williams Chukwu ◽  
Faraimunashe Chirove ◽  
fatmawati fatmawati ◽  
Princess Gatyeni
Keyword(s):  
South Africa ◽  
Optimal Control ◽  
South African ◽  
Control Measures ◽  
The Novel ◽  
Public Health Importance ◽  
Mathematical Analyses ◽  
Novel Coronavirus ◽  
Control And Management

SARS-CoV-2 (COVID-19) belongs to the beta-coronavirus family, these include; the severe acute respiratory syndrome coronavirus (SARS-CoV) and the Middle East respiratory syndrome coronavirus (MERS-CoV). Since its resurgence in South Africa in March 2020, it has lead to high mortality and thousands of people contracting the virus. In this study, we use a set of five differential equations to analyse the effects on long term dynamics of COVID-19 pandemic with optimal control measures. Mathematical analyses of the model without control were done and the basic reproduction number (R0) of the COVID-19 for the South African epidemic determined. The model steady states were also determined, and their analyses presented based on R0: We introduced permissible control measures and formulated an optimal control problem using the Pontraygain Maximum Principle. Our numerical findings suggest that joint implementation of effective mask usage, physical distancing and active screening and testing are effective measures to curtail the spread of the disease on undiagnosed humans. The results obtained in this paper are of public health importance in the control and management of the spread for the novel coronavirus, SARS-CoV-2, in South Africa.

scholarly journals Modeling Yield Losses and Fungicide Profitability for Managing Fusarium Head Blight in Brazilian Spring Wheat

2020 ◽  
Vol 110 (2) ◽  
pp. 370-378
Author(s):  
Maíra Rodrigues Duffeck ◽  
Kaique dos Santos Alves ◽  
Franklin Jackson Machado ◽  
Paul David Esker ◽  
Emerson Medeiros Del Ponte
Keyword(s):  
Fusarium Head Blight ◽  
Disease Model ◽  
Wheat Yield ◽  
Quality Parameters ◽  
Control Measures ◽  
Wheat Crop ◽  
Yield Losses ◽  
Head Blight ◽  
Yield Data ◽  
Profitability Analysis

Fusarium head blight (FHB) and wheat yield data were gathered from fungicide trials to explore their relationship. Thirty-seven studies over 9 years and 11 locations met the criteria for inclusion in the analysis: FHB index in the untreated check ≥ 5% and the range of index in a trial ≥ 4 percentage points. These studies were grouped into two baseline yields, low (Yl ≤ 3,631 kg ha−1) or high (Yh > 3,631 kg ha−1), defined based on the median of maximum yields across trials. Attainable (disease-free) yields and FHB index were predicted using a wheat crop and a disease model, respectively, in 280 simulated trials (10 planting dates in a 28-year period, 1980 to 2007) for the Passo Fundo location. The damage coefficient was then used to calculate FHB-induced yield loss (penalizing attainable yield) for each experiment. Losses were compared between periods defined as before and after FHB resurge during the early 1990s. Disease reduction from the use of one or two sprays of a triazole fungicide (tebuconazole) was also simulated, based on previous meta-analytic estimates, and the response in yield was used in a profitability analysis. Population-average intercepts but not the slopes differed significantly between Yl (2,883.6 kg ha−1) and Yh (4,419.5 kg ha−1) baseline yields and the damage coefficients were 1.60%−1 and 1.05%−1, respectively. The magnitudes and trends of simulated yield losses were in general agreement with literature reports. The risk of not offsetting the costs of one or two fungicide sprays was generally higher (>0.75) prior to FHB resurgence but fungicide profitability tended to increase in recent years, depending on the year. Our simulations allowed us to reproduce trends in historical losses, and may be further adjusted to test the effect and profitability of different control measures (host resistance, other fungicides, etc.) on quality parameters such as test weight and mycotoxin contamination, should the information become available.

scholarly journals Optimal Control and Cost Effectiveness Analysis of SIRS Malaria Disease Model with Temperature Variability Factor

2021 ◽  
Vol 53 (1) ◽  
pp. 134-163
Author(s):  
Temesgen Duressa Keno ◽  
Oluwole Daniel Makinde ◽  
Legesse Lemecha Obsu
Keyword(s):  
Optimal Control ◽  
Cost Effectiveness ◽  
Initial Conditions ◽  
Control Strategies ◽  
Disease Model ◽  
Temperature Variability ◽  
Control Measures ◽  
Basic Reproductive Number ◽  
Bed Nets ◽  
Reproductive Number

In this study, we proposed and analyzed the optimal control and cost-effectiveness strategies for malaria epidemics model with impact of temperature variability. Temperature variability strongly determines the transmission of malaria. Firstly, we proved that all solutions of the model are positive and bounded within a certain set with initial conditions. Using the next-generation matrix method, the basic reproductive number at the present malaria-free equilibrium point was computed. The local stability and global stability of the malaria-free equilibrium were depicted applying the Jacobian matrix and Lyapunov function respectively when the basic reproductive number is smaller than one. However, the positive endemic equilibrium occurs when the basic reproductive number is greater than unity. A sensitivity analysis of the parameters was conducted; the model showed forward and backward bifurcation. Secondly, using Pontryagin’s maximum principle, optimal control interventions for malaria disease reduction are described involving three control measures, namely use of insecticide-treated bed nets, treatment of infected humans using anti-malarial drugs, and indoor residual insecticide spraying. An analysis of cost-effectiveness was also conducted. Finally, based on the simulation of different control strategies, the combination of treatment of infected humans and insecticide spraying was proved to be the most efficient and least costly strategy to eradicate the disease.

scholarly journals Evaluation and Prediction of COVID-19 Prevention and Control Strategy Based on the SEIR-AQ Infectious Disease Model

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Yue Yu ◽  
Yuxing Zhou ◽  
Xiangzhong Meng ◽  
Wenfei Li ◽  
Yang Xu ◽  
...  
Keyword(s):  
Infectious Disease ◽  
Prevention And Control ◽  
Control Strategies ◽  
Disease Model ◽  
Inhibitory Effect ◽  
Euler Method ◽  
Control Measures ◽  
Infectious Disease Model ◽  
Prevention And Control Measures ◽  
And Control

Based on the SEIR model, which takes into account prevention and control measures, prevention and control awareness, and economic level and medical level indicators, this paper proposes an infectious disease model of “susceptible-exposed-infected-removed-asymptomatic-isolated” (short for SEIR-AQ) to assess and predict the development of the COVID-19 pandemic with different prevention and control strategies. The kinetic parameters of the SEIR-AQ model were obtained by fitting, and the parameters of the SEIR-AQ model were solved through the Euler method. Furthermore, the effects of different countries’ prevention and control strategies on the number of infections, the proportion of isolation, the number of deaths, and the number of recoveries were also simulated. The theoretical analysis showed that measures such as isolation for prevention and control and medical tracking isolation had a significant inhibitory effect on the development of the COVID-19 pandemic, among which stratified treatment and enhanced awareness played a key role in the rapid regression of the peak of COVID-19-infected patients. Conclusion of the Simulation. The SEIR-AQ model can be used to evaluate the development status of the COVID-19 epidemic and has some theoretical value for the prediction of COVID-19.

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