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.

scholarly journals Modeling Schistosomiasis and HIV/AIDS Codynamics

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
S. Mushayabasa ◽  
C. P. Bhunu
Keyword(s):  
Positive Impact ◽  
Asymptotically Stable ◽  
Reproduction Numbers ◽  
Therapeutic Measures ◽  
Disease Threshold ◽  
Mathematical Techniques ◽  
Manifold Theory ◽  
Parameter Values ◽  
The Impact ◽  
Hiv Aids

We formulate a mathematical model for the cointeraction of schistosomiasis and HIV/AIDS in order to assess their synergistic relationship in the presence of therapeutic measures. Comprehensive mathematical techniques are used to analyze the model steady states. The disease-free equilibrium is shown to be locally asymptotically stable when the associated disease threshold parameter known as the basic reproduction number for the model is less than unity. Centre manifold theory is used to show that the schistosomiasis-only and HIV/AIDS-only endemic equilibria are locally asymptotically stable when the associated reproduction numbers are greater than unity. The impact of schistosomiasis and its treatment on the dynamics of HIV/AIDS is also investigated. To illustrate the analytical results, numerical simulations using a set of reasonable parameter values are provided, and the results suggest that schistosomiasis treatment will always have a positive impact on the control of HIV/AIDS.

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 Model matematika penyebaran COVID-19 dengan penggunaan masker kesehatan dan karantina

2021 ◽  
Vol 2 (2) ◽  
pp. 68-79
Author(s):  
Muhammad Manaqib ◽  
Irma Fauziah ◽  
Eti Hartati
Keyword(s):  
Numerical Simulations ◽  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Endemic Equilibrium ◽  
Reproduction Numbers ◽  
Geometric Picture ◽  
Disease Free ◽  
The Basic Reproduction Number

This study developed a model for the spread of COVID-19 disease using the SIR model which was added by a health mask and quarantine for infected individuals. The population is divided into six subpopulations, namely the subpopulation susceptible without a health mask, susceptible using a health mask, infected without using a health mask, infected using a health mask, quarantine for infected individuals, and the subpopulation to recover. The results obtained two equilibrium points, namely the disease-free equilibrium point and the endemic equilibrium point, and the basic reproduction number (R0). The existence of a disease-free equilibrium point is unconditional, whereas an endemic equilibrium point exists if the basic reproduction number is more than one. Stability analysis of the local asymptotically stable disease-free equilibrium point when the basic reproduction number is less than one. Furthermore, numerical simulations are carried out to provide a geometric picture related to the results that have been analyzed. The results of numerical simulations support the results of the analysis obtained. Finally, the sensitivity analysis of the basic reproduction numbers carried out obtained four parameters that dominantly affect the basic reproduction number, namely the rate of contact of susceptible individuals with infection, the rate of health mask use, the rate of health mask release, and the rate of quarantine for infected individuals.

scholarly journals Mathematical Modeling for Prediction Dynamics of the Coronavirus Disease 2019 (COVID-19) Pandemic, Quarantine Control Measures

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1404
Author(s):  
Din Prathumwan ◽  
Kamonchat Trachoo ◽  
Inthira Chaiya
Keyword(s):  
Endemic Equilibrium ◽  
Control Measures ◽  
Single Infection ◽  
Model Parameters ◽  
Asymptotically Stable ◽  
Expected Number ◽  
Susceptible Population ◽  
Proposed Model ◽  
The Stability ◽  
Disease Free

A mathematical model for forecasting the transmission of the COVID-19 outbreak is proposed to investigate the effects of quarantined and hospitalized individuals. We analyze the proposed model by considering the existence and the positivity of the solution. Then, the basic reproduction number (R0)—the expected number of secondary cases produced by a single infection in a completely susceptible population—is computed by using the next-generation matrix to carry out the stability of disease-free equilibrium and endemic equilibrium. The results show that the disease-free equilibrium is locally asymptotically stable if R0<1, and the endemic equilibrium is locally asymptotically stable if R0>1. Numerical simulations of the proposed model are illustrated. The sensitivity of the model parameters is considered in order to control the spread by intervention strategies. Numerical results confirm that the model is suitable for the outbreak that occurred in Thailand.

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 Mathematical Approach to Investigate Stress due to Control Measures to Curb COVID-19

2022 ◽  
Vol 2022 ◽  
pp. 1-23
Author(s):  
James Nicodemus Paul ◽  
Silas Steven Mirau ◽  
Isambi Sailon Mbalawata
Keyword(s):  
Equilibrium Points ◽  
Rank Correlation ◽  
The Body ◽  
Endemic Equilibrium ◽  
Least Square ◽  
Control Measures ◽  
Model Parameters ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
The Impact

COVID-19 is a world pandemic that has affected and continues to affect the social lives of people. Due to its social and economic impact, different countries imposed preventive measures that are aimed at reducing the transmission of the disease. Such control measures include physical distancing, quarantine, hand-washing, travel and boarder restrictions, lockdown, and the use of hand sanitizers. Quarantine, out of the aforementioned control measures, is considered to be more stressful for people to manage. When people are stressed, their body immunity becomes weak, which leads to multiplying of coronavirus within the body. Therefore, a mathematical model consisting of six compartments, Susceptible-Exposed-Quarantine-Infectious-Hospitalized-Recovered (SEQIHR) was developed, aimed at showing the impact of stress on the transmission of COVID-19 disease. From the model formulated, the positivity, bounded region, existence, uniqueness of the solution, the model existence of free and endemic equilibrium points, and local and global stability were theoretically proved. The basic reproduction number ( R 0 ) was derived by using the next-generation matrix method, which shows that, when R 0 < 1 , the disease-free equilibrium is globally asymptotically stable whereas when R 0 > 1 the endemic equilibrium is globally asymptotically stable. Moreover, the Partial Rank Correlation Coefficient (PRCC) method was used to study the correlation between model parameters and R 0 . Numerically, the SEQIHR model was solved by using the Rung-Kutta fourth-order method, while the least square method was used for parameter identifiability. Furthermore, graphical presentation revealed that when the mental health of an individual is good, the body immunity becomes strong and hence minimizes the infection. Conclusively, the control parameters have a significant impact in reducing the transmission of COVID-19.

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.

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

2021 ◽  
Author(s):  
Ángel G. C. Pérez ◽  
David A. 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 analyse an extended SEIARD model with vaccination. We compute the control reproduction number $\mathcal{R}_c$ of our model and study the stability of equilibria. We show that the set of disease-free equilibria is locally asymptotically stable when $\mathcal{R}_c<1$ and unstable when $\mathcal{R}_c>1$, 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.

THE IMPACT OF MEDIA COVERAGE ON THE DYNAMICS OF INFECTIOUS DISEASE

2008 ◽  
Vol 01 (01) ◽  
pp. 65-74 ◽  
Author(s):  
YIPING LIU ◽  
JING-AN CUI
Keyword(s):  
Infectious Disease ◽  
Media Coverage ◽  
Compartment Model ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
The Impact ◽  
Globally Stable ◽  
Disease Free

In this paper, we give a compartment model to discuss the influence of media coverage to the spreading and controlling of infectious disease in a given region. The model exhibits two equilibria: a disease-free and a unique endemic equilibrium. Stability analysis of the models shows that the disease-free equilibrium is globally asymptotically stable if the reproduction number (ℝ0), which depends on parameters, is less than unity. But if ℝ0 > 1, it is shown that a unique endemic equilibrium appears, which is asymptotically stable. On a special case, the endemic equilibrium is globally stable. We discuss the role of media coverage on the spreading based on the theory results.

scholarly journals Mathematical Modelling on Double Quarantine Process in the Spread and Stability of Covid-19

2020 ◽  
Author(s):  
Jangyadatta Behera ◽  
Aswin Kumar Rauta ◽  
Yerra Shankar Rao ◽  
Sairam Patnaik
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Analytical Result ◽  
The Stability ◽  
The Impact ◽  
Disease Free

Abstract In this paper, a mathematical model is proposed on the spread and control of corona virus disease2019 (COVID19) to ascertain the impact of pre quarantine for suspected individuals having travel history ,immigrants and new born cases in the susceptible class following the lockdown or shutdown rules and adopted the post quarantine process for infected class. Set of nonlinear ordinary differential equations (ODEs) are generated and parameters like natural mortality rate, rate of COVID-19 induced death, rate of immigrants, rate of transmission and recovery rate are integrated in the scheme. A detailed analysis of this model is conducted analytically and numerically. The local and global stability of the disease is discussed mathematically with the help of Basic Reproduction Number. The ODEs are solved numerically with the help of Runge-Kutta 4th order method and graphs are drawn using MATLAB software to validate the analytical result with numerical simulation. It is found that both results are in good agreement with the results available in the existing literatures. The stability analysis is performed for both disease free equilibrium and endemic equilibrium points. The theorems based on Routh-Hurwitz criteria and Lyapunov function are proved .It is found that the system is locally asymptotically stable at disease free and endemic equilibrium points for basic reproduction number less than one and globally asymptotically stable for basic reproduction number greater than one. Finding of this study suggest that COVID-19 would remain pandemic with the progress of time but would be stable in the long-term if the pre and post quarantine policy for asymptomatic and symptomatic individuals are implemented effectively followed by social distancing, lockdown and containment.

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