scholarly journals Modeling the effect of temperature variability on malaria control strategies

2020 ◽  
Vol 15 ◽  
pp. 65
Author(s):  
Salisu M. Garba ◽  
Usman A. Danbaba
Keyword(s):  
Control Strategies ◽  
Effect Of Temperature ◽  
Bed Nets ◽  
Asymptotically Stable ◽  
Temperature Changes ◽  
Offspring Number ◽  
Local Asymptotic Stability ◽  
Reproduction Numbers ◽  
The Impact ◽  
Disease Free

In this study, a non-autonomous (temperature dependent) and autonomous (temperature independent) models for the transmission dynamics of malaria in a population are designed and rigorously analysed. The models are used to assess the impact of temperature changes on various control strategies. The autonomous model is shown to exhibit the phenomenon of backward bifurcation, where an asymptotically-stable disease-free equilibrium (DFE) co-exists with an asymptotically-stable endemic equilibrium when the associated reproduction number is less than unity. This phenomenon is shown to arise due to the presence of imperfect vaccines and disease-induced mortality rate. Threshold quantities (such as the basic offspring number, vaccination and host type reproduction numbers) and their interpretations for the models are presented. Conditions for local asymptotic stability of the disease-free solutions are computed. Sensitivity analysis using temperature data obtained from Kwazulu Natal Province of South Africa [K. Okuneye and A.B. Gumel. Mathematical Biosciences 287 (2017) 72–92] is used to assess the parameters that have the most influence on malaria transmission. The effect of various control strategies (bed nets, adulticides and vaccination) were assessed via numerical simulations.

scholarly journals Mathematical Analysis of Malaria-Schistosomiasis Coinfection Model

2016 ◽  
Vol 2016 ◽  
pp. 1-19 ◽  
Author(s):  
E. A. Bakare ◽  
C. R. Nwozo
Keyword(s):  
Numerical Simulations ◽  
Endemic Equilibrium ◽  
Model Parameters ◽  
Asymptotically Stable ◽  
Reproduction Numbers ◽  
Mathematical Techniques ◽  
Parameter Values ◽  
The Impact ◽  
Number Of Individuals ◽  
Disease Free

We formulated and analysed a mathematical model to explore the cointeraction between malaria and schistosomiasis. Qualitative and comprehensive mathematical techniques have been applied to analyse the model. The local stability of the disease-free and endemic equilibrium was analysed, respectively. However, the main theorem shows that if RMS<1, then the disease-free equilibrium is locally asymptotically stable and the phase will vanish out of the host and if RMS>1, a unique endemic equilibrium is also locally asymptotically stable and the disease persists at the endemic steady state. The impact of schistosomiasis and its treatment on malaria dynamics is also investigated. Numerical simulations using a set of reasonable parameter values show that the two epidemics coexist whenever their reproduction numbers exceed unity. Further, results of the full malaria-schistosomiasis model also suggest that an increase in the number of individuals infected with schistosomiasis in the presence of treatment results in a decrease in malaria cases. Sensitivity analysis was further carried out to investigate the influence of the model parameters on the transmission and spread of malaria-schistosomiasis coinfection. Numerical simulations were carried out to confirm our theoretical findings.

A mathematical model of cholera in a periodic environment with control actions

2020 ◽  
Vol 13 (04) ◽  
pp. 2050025
Author(s):  
G. Kolaye ◽  
I. Damakoa ◽  
S. Bowong ◽  
R. Houe ◽  
D. Békollè
Keyword(s):  
Control Strategies ◽  
Impulsive Differential Equations ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Periodic Environment ◽  
Control Actions ◽  
Number Formula ◽  
Classical Control ◽  
The Impact ◽  
Disease Free

In this paper, we studied the impact of sensitization and sanitation as possible control actions to curtail the spread of cholera epidemic within a human community. Firstly, we combined a model of Vibrio Cholerae with a generic SIRS cholera model. Classical control strategies in terms of the sensitization of population and sanitation are integrated through the impulsive differential equations. Then we presented the theoretical analysis of the model. More precisely, we computed the disease free equilibrium. We derive the basic reproduction number [Formula: see text] which determines the extinction and the persistence of the infection. We show that the trivial disease-free equilibrium is globally asymptotically stable whenever [Formula: see text], while when [Formula: see text], the trivial disease-free equilibrium is unstable and there exists a unique endemic equilibrium point which is globally asymptotically stable. Theoretical results are supported by numerical simulations, which further suggest that the control of cholera should consider both sensitization and sanitation, with a strong focus on the latter.

THE EFFECTS OF VACCINATION AND TREATMENT ON THE SPREAD OF HIV/AIDS

2004 ◽  
Vol 12 (04) ◽  
pp. 399-417 ◽  
Author(s):  
M. KGOSIMORE ◽  
E. M. LUNGU
Keyword(s):  
Equilibrium Point ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Treatment Programs ◽  
Asymptotically Stable ◽  
Reproduction Numbers ◽  
Threshold Conditions ◽  
Existence And Stability ◽  
Disease Free ◽  
Hiv Aids

This study investigates the effects of vaccination and treatment on the spread of HIV/AIDS. The objectives are (i) to derive conditions for the success of vaccination and treatment programs and (ii) to derive threshold conditions for the existence and stability of equilibria in terms of the effective reproduction number R. It is found, firstly, that the success of a vaccination and treatment program is achieved when R0t<R0, R0t<R0v and γeRVT(σ)<RUT(α), where R0t and R0v are respectively the reproduction numbers for populations consisting entirely of treated and vaccinated individuals, R0 is the basic reproduction number in the absence of any intervention, RUT(α) and RVT(σ) are respectively the reproduction numbers in the presence of a treatment (α) and a combination of vaccination and treatment (σ) strategies. Secondly, that if R<1, there exists a unique disease free equilibrium point which is locally asymptotically stable, while if R>1 there exists a unique locally asymptotically stable endemic equilibrium point, and that the two equilibrium points coalesce at R=1. Lastly, it is concluded heuristically that the stable disease free equilibrium point exists when the conditions R0t<R0, R0t<R0v and γeRVT(σ)<RUT(α) are satisfied.

scholarly journals Analysis of a malaria model with mosquito host choice and bed-net control

2015 ◽  
Vol 08 (06) ◽  
pp. 1550077 ◽  
Author(s):  
Bruno Buonomo
Keyword(s):  
Reproduction Number ◽  
Host Choice ◽  
Bed Nets ◽  
Bed Net ◽  
Host Manipulation ◽  
Host Preferences ◽  
Insecticide Treated Bed Nets ◽  
The Impact ◽  
Malaria Model ◽  
Disease Free

A malaria model is formulated which includes the enhanced attractiveness of infectious humans to mosquitoes, as result of host manipulation by malaria parasite, and the human behavior, represented by insecticide-treated bed-nets usage. The occurrence of a backward bifurcation at R0 = 1 is shown to be possible, which implies that multiple endemic equilibria co-exist with a stable disease-free equilibrium when the basic reproduction number is less than unity. This phenomenon is found to be caused by disease-induced human mortality. The global asymptotic stability of the endemic equilibrium for R0 > 1 is proved, by using the geometric method for global stability. Therefore, the disease becomes endemic for R0 > 1 regardless of the number of initial cases in both the human and vector populations. Finally, the impact on system dynamics of vector's host preferences and bed-net usage behavior is investigated.

scholarly journals Modeling Transmission of Tuberculosis with MDR and Undetected Cases

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Yongqi Liu ◽  
Zhendong Sun ◽  
Guiquan Sun ◽  
Qiu Zhong ◽  
Li Jiang ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Theoretical Analysis ◽  
Control Strategies ◽  
Multidrug Resistant ◽  
Vital Role ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Tb Control ◽  
Disease Free

This paper presents a novel mathematical model with multidrug-resistant (MDR) and undetected TB cases. The theoretical analysis indicates that the disease-free equilibrium is globally asymptotically stable ifR0<1; otherwise, the system may exist a locally asymptotically stable endemic equilibrium. The model is also used to simulate and predict TB epidemic in Guangdong. The results imply that our model is in agreement with actual data and the undetected rate plays vital role in the TB trend. Our model also implies that TB cannot be eradicated from population if it continues to implement current TB control strategies.

scholarly journals The impact of temperature changes on summer time ozone and its' precursors in the Eastern Mediterranean

2011 ◽  
Vol 11 (2) ◽  
pp. 4355-4398
Author(s):  
U. Im ◽  
K. Markakis ◽  
A. Poupkou ◽  
D. Melas ◽  
A. Unal ◽  
...  
Keyword(s):  
Urban Areas ◽  
Eastern Mediterranean ◽  
Air Pollutant ◽  
Atmospheric Composition ◽  
Effect Of Temperature ◽  
Base Case ◽  
Temperature Changes ◽  
Urban Agglomerations ◽  
Atmospheric Processes ◽  
The Impact

Abstract. Changes in temperature due to variability in meteorology and climate change are expected to significantly impact atmospheric composition. The Mediterranean is a climate sensitive region and includes megacities like Istanbul and large urban agglomerations such as Athens. The effect of temperature changes on gaseous air pollutant levels and the atmospheric processes that are controlling them in the Eastern Mediterranean are here investigated. The WRF/CMAQ mesoscale modeling system is used, coupled with the MEGAN model for the processing of biogenic volatile organic compound emissions. A set of temperature perturbations (spanning from 1 to 5 K) is applied on a base case simulation corresponding to July 2004. The results indicate that the Eastern Mediterranean basin acts as a reservoir of pollutants and their precursor emissions from large urban agglomerations. During summer, chemistry is a major sink at these urban areas near the surface, and a minor contributor at downwind areas. On average, the atmospheric processes are more effective within the first 1000 m. The response rate of biogenic emissions to temperature changes is calculated to be 9±3% K−1. Ozone concentrations respond almost linearly to the changes in the ambient temperature with rates of 1±0.1 ppb O3 K−1 for all studied urban and receptor stations except for Istanbul, where a 0.4±0.1 ppb O3 K−1 change rate is calculated, which is almost half of the domain-averaged increase of 0.9±0.1 ppb O3 K−1. The computed changes in atmospheric processes are also linearly related with temperature changes.

scholarly journals Modeling and Analysis of Population Dynamics of Examination Malpractice Among Students

2018 ◽  
Author(s):  
Chinedu Obasi ◽  
Collins Obiora ◽  
Godwin Mbah ◽  
Oluseye Olawuyi
Keyword(s):  
Mathematical Model ◽  
Population Dynamics ◽  
Social Problem ◽  
Control Strategies ◽  
Equilibrium Points ◽  
Asymptotically Stable ◽  
Awareness Campaign ◽  
Modeling And Analysis ◽  
The Impact ◽  
Insight Into

While examination malpractice has been a recognized social problem among students, the control of the phenomenon remains a challenge. In this study, we formulate a mathematical model describing the population dynamics of examination malpractice among students. Initial insight into the dynamics of the model is gained by analyzing some important mathematical features of the model such as the basic malpractice number. The malpractice-free equilibrium and endemic equilibrium points of the model are shown to be locally asymptotically stable when the basic malpractice number is less than unity. This result implies that examination malpractice can be totally eradicated among students when the basic malpractice number is less than unity. To understand the impact of controlling this social problem, we extend the model to incorporate awareness campaign and disciplinary measure as control strategies in curtailing the act. Our analysis reveals that incorporating control strategies have some influence in reducing examination malpractice among students. Further analysis indicates that considering both control strategies simultaneously yields a better result in reducing examination malpractice and examination malpractice will grow faster when control strategies are not introduced.

scholarly journals The impact of temperature changes on summer time ozone and its precursors in the Eastern Mediterranean

2011 ◽  
Vol 11 (8) ◽  
pp. 3847-3864 ◽  
Author(s):  
U. Im ◽  
K. Markakis ◽  
A. Poupkou ◽  
D. Melas ◽  
A. Unal ◽  
...  
Keyword(s):  
Urban Areas ◽  
Eastern Mediterranean ◽  
Air Pollutant ◽  
Atmospheric Composition ◽  
Effect Of Temperature ◽  
Base Case ◽  
Temperature Changes ◽  
Urban Agglomerations ◽  
Atmospheric Processes ◽  
The Impact

Abstract. Changes in temperature due to variability in meteorology and climate change are expected to significantly impact atmospheric composition. The Mediterranean is a climate sensitive region and includes megacities like Istanbul and large urban agglomerations such as Athens. The effect of temperature changes on gaseous air pollutant levels and the atmospheric processes that are controlling them in the Eastern Mediterranean are here investigated. The WRF/CMAQ mesoscale modeling system is used, coupled with the MEGAN model for the processing of biogenic volatile organic compound emissions. A set of temperature perturbations (spanning from 1 to 5 K) is applied on a base case simulation corresponding to July 2004. The results indicate that the Eastern Mediterranean basin acts as a reservoir of pollutants and their precursor emissions from large urban agglomerations. During summer, chemistry is a major sink at these urban areas near the surface, and a minor contributor at downwind areas. On average, the atmospheric processes are more effective within the first 1000 m above ground. Temperature increases lead to increases in biogenic emissions by 9±3% K−1. Ozone mixing ratios increase almost linearly with the increases in ambient temperatures by 1±0.1 ppb O3 K−1 for all studied urban and receptor stations except for Istanbul, where a 0.4±0.1 ppb O3 K−1 increase is calculated, which is about half of the domain-averaged increase of 0.9±0.1 ppb O3 K−1. The computed changes in atmospheric processes are also linearly related with temperature changes.

scholarly journals Modeling the Potential Role of Media Campaigns on the Control of Listeriosis

2020 ◽  
Author(s):  
C.W. Chukwu ◽  
F. Nyabadza
Keyword(s):  
Bacterial Pathogen ◽  
Food Contamination ◽  
Food Products ◽  
Model Parameters ◽  
Asymptotically Stable ◽  
Media Campaigns ◽  
Awareness Campaigns ◽  
The Impact ◽  
Disease Free

AbstractThe human Listeriosis infection is a food-borne disease caused by the consumption of food products contaminated by the bacterial pathogen, Listeria. In this paper, we propose a mathematical model to analyse the impact of media awareness campaigns on the spread and control of Listeriosis. The model equilibria are determined and the model has three equilibria namely; the disease-free, the Listeria-free, and the endemic equilibria. The food contamination constant (ℛf) is determined and the stability analysis shows that the disease-free steady state is locally asymptotically stable if ℛf < 1, the Listeria-free and endemic steady states are locally asymptotically stable whenever ℛf > 1. Sensitivity analysis is done to determine the model parameters that most affect the severity of the disease. Numerical simulations are carried out to determine the role of media awareness campaigns on the spread of the Listeriosis. The results show that an increase in the intensity of the media awareness campaigns and removal of contaminated food products, a decrease in the contact rate, results in fewer humans getting infected leading to disease eradication, while an increase in the depletion of media awareness campaigns results in more humans been infected with Listeriosis. These findings may significantly impact policy and decision making in the control of Listeriosis disease.

scholarly journals An extended SEIARD model for COVID-19 vaccination in Mexico: analysis and forecast

2021 ◽  
Author(s):  
Ángel G. C. Pérez ◽  
David Adeyemi Oluyori
Keyword(s):  
Global Stability ◽  
Numerical Simulations ◽  
Reproduction Number ◽  
Sufficient Condition ◽  
Asymptotically Stable ◽  
Stability Of Equilibria ◽  
The Stability ◽  
Reported Data ◽  
The Impact ◽  
Disease Free

In this study, we propose and analyze an extended SEIARD model with vaccination. We compute the control reproduction number Rc of our model and study the stability of equilibria. We show that the set of disease-free equilibria is locally asymptotically stable when Rc<1 and unstable when Rc>1, and we provide a sufficient condition for its global stability. Furthermore, we perform numerical simulations using the reported data of COVID-19 infections and vaccination in Mexico to study the impact of different vaccination, transmission and efficacy rates on the dynamics of the disease.

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