scholarly journals MODELING KENYA’S DOMESTIC RADICALIZATION LIKE A DISEASE BY INCORPORATING EFFORTS OF CLERGIES, REHABILITATION CENTERS AND JUSTICE SYSTEM

2017 ◽  
Keyword(s):  
Sensitivity Analysis ◽  
Legal System ◽  
Justice System ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Intervention Strategy ◽  
Numerical Results ◽  
Rehabilitation Centers ◽  
Analytical Results

This study presents a deterministic model for domestic radicalization process in Kenya and uses the model to assess the effect of efforts of good clergies, rehabilitation centers and legal system in lowering radicalization burden. The likelihood of other drivers of radicalization to individuals who are not religious fanatics was considered. The possibility of individuals in rehabilitated subclass quitting back to violent class was considered. The equilibrium points were computed, their stabilities investigated and important thresholds determining the progression of the radicalization computed. The sensitivity analysis of control reproduction number indicates that high intervention rates hold is likely to reduce the radicalization burden. The results indicate that use of good clergies to assist individuals’ radicalized but peaceful, to recover is the best intervention strategy. Estimated numerical results and simulations were carried to confirm analytical results.

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 Modeling the impact of early interventions on the transmission dynamics of coronavirus infection

F1000Research ◽  
2021 ◽  
Vol 10 ◽  
pp. 518
Author(s):  
Christopher Saaha Bornaa ◽  
Baba Seidu ◽  
Yakubu Ibrahim Seini
Keyword(s):  
Death Rate ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Transmission Probability ◽  
Transmission Dynamics ◽  
Early Interventions ◽  
Coronavirus Infection ◽  
The Impact ◽  
Disease Free

A deterministic model is proposed to describe the transmission dynamics of coronavirus infection with early interventions. Epidemiological studies have employed modeling to unravel knowledge that transformed the lives of families, communities, nations and the entire globe. The study established the stability of both disease free and endemic equilibria. Stability occurs when the reproduction number, R0, is less than unity for both disease free and endemic equilibrium points. The global stability of the disease-free equilibrium point of the model is established whenever the basic reproduction number R0 is less than or equal to unity. The reproduction number is also shown to be directly related to the transmission probability (β), rate at which latently infected individuals join the infected class (δ) and rate of recruitment (Λ). It is inversely related to natural death rate (μ), rate of early treatment (τ1), rate of hospitalization of infected individuals (θ) and Covid-induced death rate (σ). The analytical results established are confirmed by numerical simulation of the model.

scholarly journals Analysis of the stochastic model for predicting the novel coronavirus disease

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ndolane Sene
Keyword(s):  
Stochastic Model ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
The Novel ◽  
Stochastic Perturbations ◽  
Numerical Investigations ◽  
Rapid Spread ◽  
The World ◽  
Novel Coronavirus

Abstract In this paper, we propose a mathematical model to predict the novel coronavirus. Due to the rapid spread of the novel coronavirus disease in the world, we add to the deterministic model of the coronavirus the terms of the stochastic perturbations. In other words, we consider in this paper a stochastic model to predict the novel coronavirus. The equilibrium points of the deterministic model have been determined, and the reproduction number of our deterministic model has been implemented. The asymptotic behaviors of the solutions of the stochastic model around the equilibrium points have been studied. The numerical investigations and the graphical representations obtained with the novel stochastic model are made using the classical stochastic numerical scheme.

scholarly journals Mathematical Analysis of a Diarrhoea Model in the Presence of Vaccination and Treatment Waves with Sensitivity Analysis

2021 ◽  
Vol 25 (7) ◽  
pp. 1107-1114
Author(s):  
E.I. Akinola ◽  
B.E. Awoyemi ◽  
I.A. Olopade ◽  
O.D. Falowo ◽  
T.O. Akinwumi
Keyword(s):  
Sensitivity Analysis ◽  
Mathematical Analysis ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Runge Kutta Method ◽  
Modelling Techniques ◽  
Uniqueness And Existence ◽  
The Stability ◽  
Order Four ◽  
Disease Free

In this study, the diarrhoea model is developed based on basic mathematical modelling techniques leading to a system (five compartmental model) of ordinary differential equations (ODEs). Mathematical analysis of the model is then carried out on the uniqueness and existence of the model to know the region where the model is epidemiologically feasible. The equilibrium points of the model and the stability of the disease-free state were also derived by finding the reproduction number. We then progressed to running a global sensitivity analysis on the reproduction number with respect to all the parameters in it, and four (4) parameters were found sensitive. The work was concluded with numerical simulations on Maple 18 using Runge-Kutta method of order four (4) where the values of six (6) parameters present in the model were each varied successively while all other parameters were held constant so as to know the behaviour and effect of the varied parameter on how diarrhoea spreads in the population. The results from the sensitivity analysis and simulations were found to be in sync.

scholarly journals Modeling the impact of early interventions on the transmission dynamics of coronavirus infection

F1000Research ◽  
2021 ◽  
Vol 10 ◽  
pp. 518
Author(s):  
Christopher Saaha Bornaa ◽  
Baba Seidu ◽  
Yakubu Ibrahim Seini
Keyword(s):  
Death Rate ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Transmission Probability ◽  
Transmission Dynamics ◽  
Early Interventions ◽  
Coronavirus Infection ◽  
The Impact ◽  
Disease Free

A deterministic model is proposed to describe the transmission dynamics of coronavirus infection with early interventions. Epidemiological studies have employed modeling to unravel knowledge that transformed the lives of families, communities, nations and the entire globe. The study established the stability of both disease free and endemic equilibria. Stability occurs when the reproduction number, R0, is less than unity for both disease free and endemic equilibrium points. The global stability of the disease-free equilibrium point of the model is established whenever the basic reproduction number R0 is less than or equal to unity. The reproduction number is also shown to be directly related to the transmission probability (β), rate at which latently infected individuals join the infected class (δ) and rate of recruitment (Λ). It is inversely related to natural death rate (μ), rate of early treatment (τ1), rate of hospitalization of infected individuals (θ) and Covid-induced death rate (σ). The analytical results established are confirmed by numerical simulation of the model.

scholarly journals Optimal Control Analysis of Pneumonia and Meningitis Coinfection

2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Getachew Teshome Tilahun
Keyword(s):  
Optimal Control ◽  
Basic Reproduction Number ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Optimality System ◽  
Control Analysis ◽  
Prevention Effort ◽  
Treatment Effort ◽  
Basic Model

In this paper, we proposed a deterministic model of pneumonia-meningitis coinfection. We used a system of seven ordinary differential equations. Firstly, the qualitative behaviours of the model such as positivity of the solution, existence of the solution, the equilibrium points, basic reproduction number, analysis of equilibrium points, and sensitivity analysis are studied. The disease-free equilibrium is locally asymptotically stable if the basic reproduction number is kept less than unity, and conditions for global stability are established. Then, the basic model is extended to optimal control by incorporating four control interventions, such as prevention of pneumonia as well as meningitis and also treatment of pneumonia and meningitis diseases. The optimality system is obtained by using Pontryagin’s maximum principle. For simulation of the optimality system, we proposed five strategies to check the effect of the controls. First, we consider prevention only for both diseases, and the result shows that applying prevention control has a great impact in bringing down the expansion of pneumonia, meningitis, and their coinfection in the specified period of time. The other strategies are prevention effort for pneumonia and treatment effort for meningitis, prevention effort for meningitis and treatment effort for pneumonia, treatment effort for both diseases, and using all interventions. We obtained that each of the listed strategies is effective in minimizing the expansion of pneumonia-only, meningitis-only, and coinfectious population in the specified period of time.

scholarly journals Analysis of model for the transmission dynamics of Zika with sterile insect technique

2018 ◽  
Vol 1 ◽  
pp. 81 ◽  
Author(s):  
U.A. Danbaba ◽  
S.M. Garba
Keyword(s):  
Numerical Simulation ◽  
Sensitivity Analysis ◽  
Stability Analysis ◽  
Sterile Insect Technique ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Transmission Dynamics ◽  
Male Mosquitoes

A deterministic model for the transmission dynamics of Zika, that takes into account the aquatic and non-aquatic stages of mosquito development is constructed and rigorously analysed. The model with fraction of male mosquitoes being sterilized assumed direct (human-human) and indirect (human-mosquito-human) transmission. Stability analysis of the equilibria and sensitivity analysis of parameters associated with the computed reproduction number were presented. Numerical simulation were carried out to support the analysis.

scholarly journals Mathematical modeling and optimal intervention strategies of the COVID-19 outbreak

2021 ◽  
Author(s):  
Jayanta Mondal ◽  
Subhas Khajanchi
Keyword(s):  
Optimal Control ◽  
Basic Reproduction Number ◽  
Disease Transmission ◽  
Numerical Solutions ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Intervention Strategy ◽  
Intervention Strategies ◽  
Qualitative Behavior ◽  
The Basic Reproduction Number

Abstract 32,737,939 active cases and 438,210 deaths because of COVID-19 pandemic were recorded on 30 August 2021 in India. To end this ongoing global COVID-19 pandemic, there is an urgent need to implement multiple population-wide policies like social distancing, testing more people and contact tracing. To predict the course of the pandemic and come up with a strategy to control it effectively, a compartmental model has been established. The following six stages of infection are taken into consideration: susceptible ($S$), asymptomatic infected ($A$), clinically ill or symptomatic infected ($I$), quarantine ($Q$), isolation ($J$) and recovered ($R$), collectively termed as SAIQJR. The qualitative behavior of the model and the stability of biologically realistic equilibrium points are investigated in terms of the basic reproduction number. We performed sensitivity analysis with respect to the basic reproduction number and obtained that the disease transmission rate has an impact in mitigating the spread of diseases. Moreover, considering the non-pharmaceutical and pharmaceutical intervention strategies as control functions, an optimal control problem is implemented to mitigate the disease fatality. To reduce the infected individuals and to minimize the cost of the controls, an objective functional has been constructed and solved with the aid of Pontryagin's Maximum Principle. The implementation of optimal control strategy at the start of a pandemic tends to decrease the intensity of epidemic peaks, spreading the maximal impact of an epidemic over an extended time period. Extensive numerical simulations show that the implementation of intervention strategy has an impact in controlling the transmission dynamics of COVID-19 epidemic. Further, our numerical solutions exhibit that the combination of three controls are more influential when compared with the combination of two controls as well as single control. Therefore the implementation of all the three control strategies may help to mitigate novel coronavirus disease transmission at this present epidemic scenario.

scholarly journals Effect of Lockdown and Isolation to Suppress the COVID-19 in Bangladesh: An Epidemic Compartments Model

2020 ◽  
Author(s):  
Md. Shahidul Islam ◽  
Jannatun Irana Ira ◽  
K. M. Ariful Kabir ◽  
Md. Kamrujjaman
Keyword(s):  
Sensitivity Analysis ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Economic Stability ◽  
The Social ◽  
The World ◽  
Over Time ◽  
The Basic Reproduction Number

In the promptness of the COVID-19 outbreak, it would be very important to observe and estimate the pattern of diseases to reduce the contagious infection. To study this effect, we developed a COVID-19 analytical epidemic framework that combines with isolation and lockdown effect by incorporating five various groups of individuals. Then we analyze the model by evaluating the equilibrium points and analyzing their stability as well as determining the basic reproduction number. The extensive numerical simulations show the dynamics of a different group of the population over time. Thus, our findings based on the sensitivity analysis and the reproduction number highlight the role of outbreak of the virus that can be useful to avoid a massive collapse in Bangladesh and rest of the world. The outcome of this study concludes that outbreak will be in control which ensures the social and economic stability.

scholarly journals Cost-effectiveness analysis on measles transmission with vaccination and treatment intervention

2021 ◽  
Vol 6 (11) ◽  
pp. 12491-12527
Author(s):  
Shinta A. Rahmayani ◽  
◽  
Dipo Aldila ◽  
Bevina D. Handari
Keyword(s):  
Medical Treatment ◽  
Optimal Strategy ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Cost Effective ◽  
Qualitative Behaviour ◽  
Effectiveness Analysis ◽  
The Cost ◽  
Effective Analysis

<abstract><p>A deterministic model which describes measles' dynamic using newborns and adults first and second dose of vaccination and medical treatment is constructed in this paper. Mathematical analysis about existence of equilibrium points, basic reproduction number, and bifurcation analysis conducted to understand qualitative behaviour of the model. For numerical purposes, we estimated the parameters' values of the model using monthly measles data from Jakarta, Indonesia. Optimal control theory was applied to investigate the optimal strategy in handling measles spread. The results show that all controls succeeded in reducing the number of infected individuals. The cost-effective analysis was conducted to determine the best strategy to reduce number of infected individuals with the lowest cost of intervention. Our result indicates that the use of the first dose measles vaccine with medical treatment is the most optimal strategy to control measles transmission.</p></abstract>

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