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 Dynamical System Analysis of a Lassa Fever Model with Varying Socioeconomic Classes

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Ifeanyi Sunday Onah ◽  
Obiora Cornelius Collins
Keyword(s):  
Disease Transmission ◽  
System Analysis ◽  
Lassa Fever ◽  
West African ◽  
Sensitivity Analyses ◽  
Model Parameters ◽  
Lassa Virus ◽  
African Countries ◽  
Patch Model ◽  
Viral Illness

Lassa fever is an animal-borne acute viral illness caused by Lassa virus. It poses a serious health challenge around the world today, especially in West African countries like Ghana, Benin, Guinea, Liberia, Mali, Sierra Leone, and Nigeria. In this work, we formulate a multiple-patch Lassa fever model, where each patch denotes a socioeconomic class (SEC). Some of the important epidemiological features such as basic reproduction number of the model were determined and analysed accordingly. We further investigated how varying SECs affect the transmission dynamics of Lassa fever. We analysed the required state at which each SEC is responsible in driving the Lassa fever disease outbreak. Sensitivity analyses were carried out to determine the importance of model parameters to the disease transmission and prevalence. We carried out numerical simulation to support our analytical results. Finally, we extend some of the results of the 2-patch model to the general n -patch model.

scholarly journals A Mathematical Model For Lassa Fever Transmission Dynamics With Impacts of Control Measures: Analysis And Simulation

2021 ◽  
Vol 2 (2) ◽  
pp. 19-28
Author(s):  
Oke Isaiah Idisi ◽  
Tunde Tajudeen Yusuf
Keyword(s):  
Disease Transmission ◽  
Control Strategies ◽  
Disease Outbreaks ◽  
Lassa Fever ◽  
Control Measures ◽  
Transmission Dynamics ◽  
Effective Control ◽  
Lassa Virus ◽  
Long Run ◽  
Globally Stable

Lassa Fever, caused by Lassa virus, is a vector-host transmitted infectious disease whose prevalence has been on the upsurge over the past few decades. Thus, considering the grave implications of the continuous spread of the disease, an epidemic model was developed to describe the disease transmission dynamics with impacts of proposed control measures. This is to help inform effective control strategies that would successfully curtail and contain the disease in its endemic areas. The model is qualitatively analyzed in order to contextualize the long run behavior of the model while the model associated basic reproduction number $(\mathcal{R}_0)$ is derived. The model analysis reveals that the disease-free equilibrium is locally and globally stable whenever $ \mathcal{R}_0 < 1 $ and the disease prevalence would be high as long as $ \mathcal{R}_0 > 1 $. Finally, the model is numerically solved and simulated for different scenarios of the disease outbreaks while the findings from simulations are discussed.

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 Controlling Rabies Epidemics in Nepal with Limited Resources: Optimal Control Theory Approach

2020 ◽  
Vol 99 (99) ◽  
pp. 1-18
Author(s):  
Buddhi Pantha ◽  
Hem Joshi ◽  
Naveen Vaidya
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Control Measures ◽  
Health Concern ◽  
Limited Resources ◽  
Extended Model ◽  
Theory Approach ◽  
Dependent Manner ◽  
Optimal Control Strategy

In many developing countries, including Nepal, rabies epidemics constitute a serious public health concern, partly because of limited resources for proper implementation of control measures. In this study, we develop an extended model by incorporating various controls into the transmission dynamics model with both dog and jackal vectors. We apply the optimal control theory on the developed model system to identify optimal control strategy for mitigating rabies burden in Nepal with limited resources. Among the potential control strategies, human vaccination, dog vaccination, dog culling, dog sterilization, and jackal vaccination, considered in this study, our results show that a combination of dog vaccination and dog culling is the most effective strategy to control rabies in Nepal. Our optimal control solutions provide the strategy for optimal implementation of these controls to suppress rabies prevalence among dogs and jackals of Nepal using a minimum cost associated with controls. We found that given limited resources, implementing controls in a time-dependent manner with a higher level at the beginning of the outbreaks and reducing them during later part of the epidemics can provide maximum benefits.

scholarly journals Knowledge of Lassa Fever Disease and Its Risk Factors Among Rural People in a Nigerian Community

Proceedings ◽  
2020 ◽  
Vol 45 (1) ◽  
pp. 9
Author(s):  
Abdulrazaq Abdullahi Gobir ◽  
Clara Ladi Ejembi ◽  
Aliyu Abubakar Alhaji ◽  
Muhammad Bello Garba ◽  
Chinedu John -Camillus Igboanusi ◽  
...  
Keyword(s):  
Risk Factors ◽  
Rural Areas ◽  
Disease Transmission ◽  
Public Awareness ◽  
Lassa Fever ◽  
Lassa Virus ◽  
African Countries ◽  
Public Health Importance ◽  
Cross Sectional ◽  
Effective Prevention

Introduction: Lassa fever disease (LFD) is an acute viral haemorrhagic fever caused by Lassa virus. It is a disease of public health importance in West Africa and a global health threat. It is endemic in some West African countries like Benin, Ghana, Guinea, Liberia, Mali, Sierra Leone, and Nigeria, where an estimated 300,000 to 500,000 cases occur every year with an estimated 5000 annual deaths. Persons living in rural areas and health care workers are at greatest risk. Public awareness and knowledge of the LFD and its risk factors are some of the important factors that determine disease transmission and success of preventive/control efforts. This study was therefore conducted to assess LFD-related awareness and knowledge in Gangara, a rural agrarian community in Giwa Local Government Area of Kuduna State, NorthWest Nigeria. Methods: A cross-sectional, community based descriptive study conducted in Gangara community. An interviewer- administered questionnaire was used to collect data from 556 adult respondents, selected using systematic random sampling technique. Data was analyzed using SPSS (version 20). Results: A majority of the respondents were females (52.9%) with a mean age of 37.0 ± 15.2. The level of awareness of LFD was high (66.7%) among respondents and there was a statistically significant association between awareness of LFD and not having any form of education (P < 0.00). However, most of the respondents (79.0%) have poor knowledge of LFD. Knowledge of risk factors for LFD was also poor with 59.4% not knowing that drying grains and foodstuffs on the ground is a risk factor for LFD. Conclusions: Awareness of the disease was quite high but knowledge of the disease and its risk factors was poor. For effective prevention of future outbreaks, the community needs to be properly educated on LFD and its risk factors.

TRANSMISSION DYNAMICS AND OPTIMAL CONTROL OF AN INFLUENZA MODEL WITH QUARANTINE AND TREATMENT

2012 ◽  
Vol 05 (03) ◽  
pp. 1260011 ◽  
Author(s):  
WEI-WEI SHI ◽  
YUAN-SHUN TAN
Keyword(s):  
Optimal Control ◽  
Disease Transmission ◽  
Reproduction Number ◽  
Influenza Pandemic ◽  
Control Measures ◽  
Globally Asymptotically Stable ◽  
Number Formula ◽  
Parameter Values ◽  
The Impact ◽  
Disease Free

We develop an influenza pandemic model with quarantine and treatment, and analyze the dynamics of the model. Analytical results of the model show that, if basic reproduction number [Formula: see text], the disease-free equilibrium (DFE) is globally asymptotically stable, if [Formula: see text], the disease is uniformly persistent. The model is then extended to assess the impact of three anti-influenza control measures, precaution, quarantine and treatment, by re-formulating the model as an optimal control problem. We focus primarily on controlling disease with a possible minimal the systemic cost. Pontryagin's maximum principle is used to characterize the optimal levels of the three controls. Numerical simulations of the optimality system, using a set of reasonable parameter values, indicate that the precaution measure is more effective in reducing disease transmission than the other two control measures. The precaution measure should be emphasized.

scholarly journals Control measures following a case of imported Lassa fever from Togo, North Rhine Westphalia, Germany, 2016

2017 ◽  
Vol 22 (39) ◽  
Author(s):  
Clara Lehmann ◽  
Matthias Kochanek ◽  
Diana Abdulla ◽  
Stephan Becker ◽  
Boris Böll ◽  
...  
Keyword(s):  
Virus Infection ◽  
Infection Control ◽  
Clinical Signs ◽  
Index Patient ◽  
The United States ◽  
Lassa Fever ◽  
Control Measures ◽  
University Hospital ◽  
Lassa Virus ◽  
Infection Control Measures

In a patient transferred from Togo to Cologne, Germany, Lassa fever was diagnosed 12 days post mortem. Sixty-two contacts in Cologne were categorised according to the level of exposure, and gradual infection control measures were applied. No clinical signs of Lassa virus infection or Lassa specific antibodies were observed in the 62 contacts. Thirty-three individuals had direct contact to blood, other body fluids or tissue of the patients. Notably, with standard precautions, no transmission occurred between the index patient and healthcare workers. However, one secondary infection occurred in an undertaker exposed to the corpse in Rhineland-Palatinate, who was treated on the isolation unit at the University Hospital of Frankfurt. After German authorities raised an alert regarding the imported Lassa fever case, an American healthcare worker who had cared for the index patient in Togo, and who presented with diarrhoea, vomiting and fever, was placed in isolation and medevacked to the United States. The event and the transmission of Lassa virus infection outside of Africa underlines the need for early diagnosis and use of adequate personal protection equipment (PPE), when highly contagious infections cannot be excluded. It also demonstrates that larger outbreaks can be prevented by infection control measures, including standard PPE.

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 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.

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