scholarly journals Global Stability of Malaria Transmission Dynamics Model with Logistic Growth

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Abadi Abay Gebremeskel
Keyword(s):  
Sensitivity Analysis ◽  
Global Stability ◽  
Malaria Transmission ◽  
Equilibrium Points ◽  
Transmission Dynamics ◽  
Logistic Growth ◽  
Asymptotically Stable ◽  
Dynamics Model ◽  
Globally Asymptotically Stable ◽  
The Impact

Mathematical models become an important and popular tools to understand the dynamics of the disease and give an insight to reduce the impact of malaria burden within the community. Thus, this paper aims to apply a mathematical model to study global stability of malaria transmission dynamics model with logistic growth. Analysis of the model applies scaling and sensitivity analysis and sensitivity analysis of the model applied to understand the important parameters in transmission and prevalence of malaria disease. We derive the equilibrium points of the model and investigated their stabilities. The results of our analysis have shown that if R0≤1, then the disease-free equilibrium is globally asymptotically stable, and the disease dies out; if R0>1, then the unique endemic equilibrium point is globally asymptotically stable and the disease persists within the population. Furthermore, numerical simulations in the application of the model showed the abrupt and periodic variations.

scholarly journals Global Stability and Optimal Control of Dengue with Two Coexisting Virus Serotypes

MATEMATIKA ◽  
2019 ◽  
Vol 35 (4) ◽  
pp. 149-170
Author(s):  
Afeez Abidemi ◽  
Rohanin Ahmad ◽  
Nur Arina Bazilah Aziz
Keyword(s):  
Optimal Control ◽  
Global Stability ◽  
Disease Transmission ◽  
Deterministic Model ◽  
Control Strategies ◽  
Equilibrium Points ◽  
Effective Control ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Boundary Equilibrium

This study presents a two-strain deterministic model which incorporates Dengvaxia vaccine and insecticide (adulticide) control strategies to forecast the dynamics of transmission and control of dengue in Madeira Island if there is a new outbreak with a different virus serotypes after the first outbreak in 2012. We construct suitable Lyapunov functions to investigate the global stability of the disease-free and boundary equilibrium points. Qualitative analysis of the model which incorporates time-varying controls with the specific goal of minimizing dengue disease transmission and the costs related to the control implementation by employing the optimal control theory is carried out. Three strategies, namely the use of Dengvaxia vaccine only, application of adulticide only, and the combination of Dengvaxia vaccine and adulticide are considered for the controls implementation. The necessary conditions are derived for the optimal control of dengue. We examine the impacts of the control strategies on the dynamics of infected humans and mosquito population by simulating the optimality system. The disease-freeequilibrium is found to be globally asymptotically stable whenever the basic reproduction numbers associated with virus serotypes 1 and j (j 2 {2, 3, 4}), respectively, satisfy R01,R0j 1, and the boundary equilibrium is globally asymptotically stable when the related R0i (i = 1, j) is above one. It is shown that the strategy based on the combination of Dengvaxia vaccine and adulticide helps in an effective control of dengue spread in the Island.

scholarly journals Analysis of the Model on the Effect of Seasonal Factors on Malaria Transmission Dynamics

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Victor Yiga ◽  
Hasifa Nampala ◽  
Julius Tumwiine
Keyword(s):  
Malaria Transmission ◽  
Basic Reproduction Number ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Current Control ◽  
Transmission Dynamics ◽  
Mosquito Vector ◽  
The Impact ◽  
The Basic Reproduction Number

Malaria is one of the world’s most prevalent epidemics. Current control and eradication efforts are being frustrated by rapid changes in climatic factors such as temperature and rainfall. This study is aimed at assessing the impact of temperature and rainfall abundance on the intensity of malaria transmission. A human host-mosquito vector deterministic model which incorporates temperature and rainfall dependent parameters is formulated. The model is analysed for steady states and their stability. The basic reproduction number is obtained using the next-generation method. It was established that the mosquito population depends on a threshold value θ , defined as the number of mosquitoes produced by a female Anopheles mosquito throughout its lifetime, which is governed by temperature and rainfall. The conditions for the stability of the equilibrium points are investigated, and it is shown that there exists a unique endemic equilibrium which is locally and globally asymptotically stable whenever the basic reproduction number exceeds unity. Numerical simulations show that both temperature and rainfall affect the transmission dynamics of malaria; however, temperature has more influence.

scholarly journals Stability and global sensitivity analysis of the transmission dynamics of malaria with relapse and ignorant infected humans

2022 ◽  
Author(s):  
Yves Tinda Mangongo ◽  
Joseph-Désiré Kyemba Bukweli ◽  
Justin Dupar Busili Kampempe ◽  
Rostin Matendo Mabela ◽  
Justin Manango Wazute Munganga
Keyword(s):  
Sensitivity Analysis ◽  
Recovery Rate ◽  
Global Sensitivity Analysis ◽  
Rank Correlation ◽  
Latin Hypercube Sampling ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Global Sensitivity ◽  
Partial Rank Correlation

Abstract In this paper we present a more realistic mathematical model for the transmission dynamics of malaria by extending the classical SEIRS scheme and the model of Hai-Feng Huo and Guang-Ming Qiu [21] by adding the ignorant infected humans compartment. We analyze the global asymptotically stabilities of the model by the use of the basic reproduction number R_0 and we prove that when R_0≦1, the disease-free equilibrium is globally asymptotically stable. That is malaria dies out in the population. When R_0>1, there exists a co-existing unique endemic equilibrium which is globally asymptotically stable. The global sensitivity analysis have been done through the partial rank correlation coefficient using the samples generated by the use of latin hypercube sampling method and shows that the most influence parameters in the spread of malaria are the proportion θ of infectious humans who recover and the recovery rate γ of infectious humans. In order to eradicate malaria, we have to decrease the number of ignorant infected humans by testing peoples and treat them. Numerical simulations show that malaria can be also controlled or eradicated by increasing the recovery rate γ of infectious humans, decreasing the number of ignorant infected humans and decreasing the average number n of mosquito bites.

scholarly journals Modeling Tuberculosis Among Healthcare Workers

2019 ◽  
Vol 5 (2) ◽  
pp. 186-196
Author(s):  
T.S. Faniran ◽  
A.O. Falade ◽  
T.O. Alakija
Keyword(s):  
Sensitivity Analysis ◽  
Equilibrium Point ◽  
Healthcare Workers ◽  
Compliance Rate ◽  
Transmission Dynamics ◽  
Infectious Period ◽  
Model Parameters ◽  
Asymptotically Stable ◽  
Susceptible Population ◽  
The Impact

AbstractA mathematical model for transmission dynamics of tuberculosis among healthcare workers is formulated. Tuberculosis is an airborne disease caused by Mycobacterium tuberculosis bacteria that affect the lungs of a host. Previous research had concentrated on mathematical modeling of transmission dynamics of tuberculosis without considering the impact of compliance rate to particulate respirator by healthcare workers on the transmission. Therefore, how compliance rate to particulate respirator reduces the transmission of tuberculosis is an active question, and we develop a new system of ordinary differential equations that explicitly explores the impact of compliance rate to particulate respirator by healthcare workers upon transmission. Rigorous analysis of the model shows that the disease-free equilibrium point is locally asymptotically stable when the basic reproduction number, Ro < 1. This is established through the analysis of characteristic equation. Basic reproduction, Ro is the number of new cases that an existing case generates on average over the infectious period in a susceptible population. We also show that the endemic equilibrium point is locally asymptotically stable for Ro > 1, by using Routh-Hurwitz criteria for stability. Sensitivity analysis is carried out to determine the relative importance of the model parameters to the disease transmission. The result of the sensitivity analysis shows that the most sensitive parameter is β (Human-to-human transmission rate), followed by Λ (Human recruitment rate). Also, the result shows that increase in ψ (compliance rate to particulate respirator by healthcare workers) leads to decrease in Ro which reduces tuberculosis spread among healthcare workers.

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 Modeling the Effect of External Computers and Removable Devices on a Computer Network with Heterogeneous Immunity

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Walaa S. Bahashwan ◽  
Salma M. Al-Tuwairqi
Keyword(s):  
Sensitivity Analysis ◽  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Computer Network ◽  
Asymptotically Stable ◽  
Virus Spread ◽  
Globally Asymptotically Stable ◽  
Virus Prevalence ◽  
The Impact ◽  
Insight Into

This paper intends to investigate the impact of external computers and removable devices on virus spread in a network with heterogeneous immunity. For that purpose, a new dynamical model is presented and discussed. Theoretical analysis reveals the existence of a unique viral equilibrium that is locally and globally asymptotically stable with no criteria. This result implies that efforts to eliminate viruses are not possible. Therefore, sensitivity analysis is performed to have more insight into parameters’ impact on virus prevalence. As a result, strategies are suggested to contain virus spread to an acceptable level. Finally, to rationalize the analytical results, we execute some numerical simulations.

Assessing the impact of transmissibility on a cluster-based COVID-19 model in India

2021 ◽  
pp. 2141002
Author(s):  
Tanvi ◽  
Mohammad Sajid ◽  
Rajiv Aggarwal ◽  
Ashutosh Rajput
Keyword(s):  
Reproduction Number ◽  
Transmission Rate ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Nonlinear Mathematical Model ◽  
Globally Asymptotically Stable ◽  
Number Formula ◽  
The Stability ◽  
The Impact ◽  
Disease Free

In this paper, we have proposed a nonlinear mathematical model of different classes of individuals for coronavirus (COVID-19). The model incorporates the effect of transmission and treatment on the occurrence of new infections. For the model, the basic reproduction number [Formula: see text] has been computed. Corresponding to the threshold quantity [Formula: see text], the stability of endemic and disease-free equilibrium (DFE) points are determined. For [Formula: see text], if the endemic equilibrium point exists, then it is locally asymptotically stable, whereas the DFE point is globally asymptotically stable for [Formula: see text] which implies the eradication of the disease. The effects of various parameters on the spread of COVID-19 are discussed in the segment of sensitivity analysis. The model is numerically simulated to understand the effect of reproduction number on the transmission dynamics of the disease COVID-19. From the numerical simulations, it is concluded that if the reproduction number for the coronavirus disease is reduced below unity by decreasing the transmission rate and detecting more number of infectives, then the epidemic can be eradicated from the population.

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.

scholarly journals Mathematical Modeling and Analysis of Transmission Dynamics and Control of Schistosomiasis

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Ebrima Kanyi ◽  
Ayodeji Sunday Afolabi ◽  
Nelson Owuor Onyango
Keyword(s):  
Equilibrium Point ◽  
Control Strategies ◽  
Equilibrium Points ◽  
Threshold Value ◽  
Endemic Equilibrium ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Modeling And Analysis ◽  
Disease Free

This paper presents a mathematical model that describes the transmission dynamics of schistosomiasis for humans, snails, and the free living miracidia and cercariae. The model incorporates the treated compartment and a preventive factor due to water sanitation and hygiene (WASH) for the human subpopulation. A qualitative analysis was performed to examine the invariant regions, positivity of solutions, and disease equilibrium points together with their stabilities. The basic reproduction number, R 0 , is computed and used as a threshold value to determine the existence and stability of the equilibrium points. It is established that, under a specific condition, the disease-free equilibrium exists and there is a unique endemic equilibrium when R 0 > 1 . It is shown that the disease-free equilibrium point is both locally and globally asymptotically stable provided R 0 < 1 , and the unique endemic equilibrium point is locally asymptotically stable whenever R 0 > 1 using the concept of the Center Manifold Theory. A numerical simulation carried out showed that at R 0 = 1 , the model exhibits a forward bifurcation which, thus, validates the analytic results. Numerical analyses of the control strategies were performed and discussed. Further, a sensitivity analysis of R 0 was carried out to determine the contribution of the main parameters towards the die out of the disease. Finally, the effects that these parameters have on the infected humans were numerically examined, and the results indicated that combined application of treatment and WASH will be effective in eradicating schistosomiasis.

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