A Deterministic Analysis of the Effectiveness of Non-Clinical Approaches in the Control of Transimission of Schistosomiasis: Case Study of Mwea Irrigation Scheme, Kenya

Schistosomiasis commonly known as bilharzia is regarded by W.H.O as a neglected tropical disease. It affects the intestines and the urinary system preferentially, but can harm other systems in the body. The disease is a health concern among majority of the population in Mwea irrigation scheme in Kenya and indeed other tropical countries. This paper documents a deterministic analysis of the effectiveness of non-clinical approaches in the control of transmission of schistosomiasis in the region. A SIR based mathematical model that incorporates media campaigns as a control strategy of reducing transmission of the disease is used. The model considers behavior patterns of hosts as the main process of transmission of the disease. The dynamics of these processes is expressed in terms of ordinary differential equations deduced from the human behavior patterns that contribute to the spread of the disease. The reproduction number R0 and equilibrium points both DFE and EE are obtained. The stabilities of these equilibrium points are analyzed in reference to the reproduction number (R0). Secondary data is used in the mathematical model developed and in the prediction of the dynamics estimated in the model for a period of five years. Numerical simulation was carried out and results represented graphically. The results of the simulation show that the infection decreased from 75108 to about 35000 and the susceptible from 325142 to 50000 respectively in a period of five years. From the analysis, the DFE point is asymptotically stable when R_0<1.Sensitivity analysis of parameters was carried out using partial differentiation. The results show that the sensitivity index of most parameters are inversely proportional to R0 which will reduce schistosomiasis infection. From the results, incorporation of media campaigns as a control strategy significantly reduces transmission of the disease. The results will be useful to MOH to enhance media campaigns to prevent spread of schistosomiasis in Mwea Irrigation scheme and other endemic areas.

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Investigating the Role of Environmental Transmission in COVID-19 Dynamics: A Mathematical Model Based Study

10.21203/rs.3.rs-32476/v1 ◽

2020 ◽

Author(s):

Ibrahim M. ELmojtaba ◽

Fatma Al-Musalhi ◽

Asma Al-Ghassani ◽

Nasser Al-Salti

Keyword(s):

Mathematical Model ◽

Disease Transmission ◽

Reproduction Number ◽

Equilibrium Points ◽

Transmission Dynamics ◽

Model Parameters ◽

Environmental Transmission ◽

Estimated Parameters ◽

Existence And Stability

Abstract A mathematical model with environmental transmission has been proposed and analyzed to investigate its role in the transmission dynamics of the ongoing COVID-19 outbreak. Two expressions for the basic reproduction number R0 have been analytically derived using the next generation matrix method. The two expressions composed of a combination of two terms related to human to human and environment to human transmissions. The value of R0 has been calculated using estimated parameters corresponding to two datasets. Sensitivity analysis of the reproduction number to the corresponding model parameters has been carried out. Existence and stability analysis of disease free and endemic equilibrium points have been presented in relation with the obtained expressions of R0. Numerical simulations to demonstrate the effect of some model parameters related to environmental transmission on the disease transmission dynamics have been carried out and the results have been demonstrated graphically.

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DYNAMICS OF ENVIRONMENTAL POLLUTIONTHROUGH VEHICLES

International Journal of Engineering Technologies and Management Research ◽

10.29121/ijetmr.v5.i4.2018.206 ◽

2020 ◽

Vol 5 (4) ◽

pp. 38-47

Author(s):

Nita Shah ◽

Shreya Patel ◽

Moksha Satia ◽

Foram Thakkar

Keyword(s):

Numerical Simulation ◽

Mathematical Model ◽

Air Pollution ◽

Stability Analysis ◽

Reproduction Number ◽

Equilibrium Points ◽

System Stability ◽

System Stability Analysis ◽

Almost All ◽

Day By Day

In today’s time as air pollution is increasing day by day the use of non-polluted has to be increased in almost all nooks and corner of the countries. In this paper a mathematical model is developed to analyse environmental pollution through polluted and non-polluted vehicles. Basic reproduction number has been calculated which will the decide the behavior of the system. Stability analysis has been carried out at equilibrium points. Numerical simulation is done to analyse the result for various compartments.

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Stability and optimal control in a mathematical model of online game addiction

Filomat ◽

10.2298/fil1917691l ◽

2019 ◽

Vol 33 (17) ◽

pp. 5691-5711 ◽

Cited By ~ 2

Author(s):

Tingting Li ◽

Youming Guo

Keyword(s):

Mathematical Model ◽

Optimal Control ◽

Maximum Principle ◽

Control Strategy ◽

Reproduction Number ◽

Direct Transfer ◽

Online Game ◽

Optimal Control Strategy ◽

Game Addiction ◽

The Basic Reproduction Number

In this paper, we construct an online game addiction model(including susceptible, infective, professional and quitting compartments). We also consider that the direct transfer from the susceptible individuals to the professional individuals. Some properties of the model are derived by the basic reproduction number R0 and stability of all kinds of equilibria is obtained. Then we use Pontriagin?s maximum principle to solve the optimal control strategy. Finally, Numerical simulations are also conducted in the analytic results.

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Analysis of the SARS-CoV-2 Outbreak in Northern Cyprus using a Mathematical Model

10.21203/rs.3.rs-28213/v1 ◽

2020 ◽

Author(s):

Tamer Sanlidag ◽

Nazife Sultanoglu ◽

Bilgen Kaymakamzade ◽

Evren Hincal ◽

Murat Sayan ◽

...

Keyword(s):

Mathematical Model ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Equilibrium Points ◽

Real Data ◽

Northern Cyprus ◽

The Stability ◽

Disease Free ◽

The Basic Reproduction Number

Abstract The present study studied the dynamics of SARS-CoV-2 in Northern-Cyprus (NC) by using real data and a designed mathematical model. The model consisted of two equilibrium points, which were disease-free and epidemic. The stability of the equilibrium points was determined by the magnitude of the basic reproduction number (𝑹𝟎). If 𝑹𝟎 < 1, the disease eventually disappears, if 𝑹𝟎 ≥ 1, the presence of an epidemic is stated. 𝑹𝟎 has been calculated patient zero, with a range of 2.38 to 0.65. Currently, the 𝑹𝟎 for NC was found to be 0.65, indicating that NC is free from the SARS-CoV-2 epidemic.

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Analysis of the SARS-CoV-2 Outbreak in Northern Cyprus using a Mathematical Model

10.21203/rs.3.rs-28704/v1 ◽

2020 ◽

Author(s):

Tamer Sanlidag ◽

Nazife Sultanoglu ◽

Bilgen Kaymakamzade ◽

Evren Hincal ◽

Murat Sayan ◽

...

Keyword(s):

Mathematical Model ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Equilibrium Points ◽

Real Data ◽

Northern Cyprus ◽

The Stability ◽

Disease Free ◽

The Basic Reproduction Number

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Government control in increasing vehicles taxpayer compliance

Technium Social Sciences Journal ◽

10.47577/tssj.v26i1.5213 ◽

2021 ◽

Vol 26 ◽

pp. 502-513

Author(s):

Diah Anggeraini Hasri ◽

Zulkieflimansyah Zulkieflimansyah ◽

Muhammad Nurjihadi ◽

Nova Adhitya Ananda ◽

Lukmanul Hakim

Keyword(s):

Mathematical Model ◽

Regression Analysis ◽

Differential Equations ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Sensitivity Index ◽

Control Parameters ◽

Government Control ◽

Analysis Tools ◽

The Basic Reproduction Number

This study aims to determine the dynamics of taxpayer compliance from time to time by using a mathematical model. This study uses two analysis tools, namely differential equations, to create a model of taxpayer compliance and Moderated Regression Analysis to determine the effect of moderating government control on increasing taxpayer compliance. This study indicates that government control can reduce the number of non-compliant taxpayers by looking at the sensitivity index. The results of the sensitivity index of government control parameters can reduce the basic reproduction number. Statistically, it is also proven that the moderation of government control can strengthen the effect of awareness on taxpayer compliance by 82.5%.

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Mathematical Modelling and Control of COVID-19 Transmission in the Presence of Exposed Immigrants

Communication in Biomathematical Sciences ◽

10.5614/cbms.2021.4.2.2 ◽

2021 ◽

Vol 4 (2) ◽

pp. 93-105

Author(s):

Reuben Iortyer Gweryina ◽

Chinwendu Emilian Madubueze ◽

Martins Afam Nwaokolo

Keyword(s):

Mathematical Model ◽

Reproduction Number ◽

Equilibrium Points ◽

Horizontal Transmission ◽

Endemic Equilibrium ◽

Asymptotically Stable ◽

Susceptible Population ◽

Continuous Mixing ◽

And Control ◽

The Impact

In this paper, a mathematical model for COVID-19 pandemic that spreads through horizontal transmission in the presence of exposed immigrants is studied. The model has equilibrium points, notably, COVID-19-free equilibrium and COVID-19-endemic equilibrium points. The model exhibits a basic reproduction number, R0 which determines the elimination and persistence of the disease. It was found that when R0 < 1, then the equilibrium becomes locally asymptotically stable and endemic equilibrium does not exists. However, when R0 > 1, the equilibrium is found to be stable globally. This implies that continuous mixing of exposed immigrants with the susceptible population will make the eradication of COVID-19 difficult and endemic in the community. The system is also proved qualitatively to experience transcritical bifurcation close to the COVID-19-free equilibrium at the point R0 = 1. Numerically, the model is used to investigate the impact of certain other relevant parameters on the spread of COVID-19 and how to curtail their effect.

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ANALISIS MODEL MATEMATIKA PENYEBARAN PENYAKIT H1N1 DENGAN TINGKAT KEJADIAN TERSATURASI

Journal of Mathematics Education and Science ◽

10.32665/james.v1iapril.14 ◽

2018 ◽

Vol 1 (April) ◽

pp. 29-33

Author(s):

M. Ivan Ariful Fathoni

Keyword(s):

Mathematical Model ◽

Equilibrium Point ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Equilibrium Points ◽

Infected Individual ◽

Swine Flu ◽

Occurrence Rate ◽

Model Formation ◽

The Basic Reproduction Number

Swine flu is an acute respiratory infection that attacks the body's organs especially the lungs. The disease is caused by Influenza Virus Type A, type H1N1. In this article constructed mathematical model of the spread of H1N1 disease. Mathematical model that created the model Susceptible, Exposed, Infective, and Treatment. The existence of behavior change and influence of infected individual density become the reason of model formation with saturation occurrence rate. From the dynamic analysis, the model has two equilibrium points, that is, a stable equilibrium free equilibrium point when the basic reproduction number is less or equal to one, and an endemic equilibrium point that exists and is stable when the basic reproduction number is greater than one. Finally, the results of the analysis prove the control of the spread of disease into a disease-free state. Flu babi adalah infeksi saluran pernapasan akut yang menyerang organ tubuh terutama paru-paru. Penyakit ini disebabkan oleh Virus Influenza tipe A, jenis H1N1. Pada artikel ini dikonstruksi model matematika penyebaran penyakit H1N1. Model matematika yang dibuat yaitu model Susceptible, Exposed, Infective, dan Treatment. Adanya perubahan perilaku dan pengaruh kepadatan individu terinfeksi menjadi alasan pembentukan model dengan tingkat kejadian tersaturasi. Dari hasil analisis dinamik, model memiliki dua titik kesetimbangan, yaitu titik kesetimbangan bebas penyakit yang bersifat stabil saat bilangan reproduksi dasar bernilai lebih kecil atau sama dengan satu, dan titik kesetimbangan endemi yang eksis dan bersifat stabil saat bilangan reproduksi dasar bernilai lebih besar dari satu. Pada akhirnya, hasil analisis membuktikan adanya kontrol penyebaran penyakit menjadi keadaan bebas penyakit.

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Sensitifity Analysis of Mathematical Model of Coronavirus Disease (COVID-19) Transmission

CAUCHY ◽

10.18860/ca.v6i2.9165 ◽

2020 ◽

Vol 6 (2) ◽

pp. 91 ◽

Cited By ~ 2

Author(s):

Resmawan Resmawan ◽

Lailany Yahya

Keyword(s):

Mathematical Model ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Sensitivity Index ◽

Contact Rate ◽

Movement Rate ◽

Exposed Individual ◽

The Mathematical Model ◽

Positive Index ◽

Disease Free

The study was aimed to introduce a new model construction regarding the transmission of Coronavirus Disease (henceforth, COVID-19) in human population. The mathematical model was constructed by taking into consideration several epidemiology parameters that are closely identical with the real condition. The study further conducted an analysis on the model by identifying the endemicity parameters of COVID-19, i.e., the presence of disease-free equilibrium (DFE) point and basic reproduction number. The next step was to carry out sensitivity analysis to find out which parameter is the most dominant to affect the disease’s endemicity. The results revealed that the parameters 𝜂, 𝜁𝑠𝑒, 𝛼,, and 𝜎 in sequence showed the most dominant sensitivity index towards the basic reproduction number. Moreover, the results indicated positive index in parameters 𝜂 and 𝜁𝑠𝑒 that represented transmission chances during contact as well as contact rate between vulnerable individuals and exposed individual. This suggests that an increase in the previous parameter value could potentially enlarge the endemicity of COVID-19. On the other hand, parameters 𝛼 and 𝜎, representing movement rate of exposed individuals to the quarantine class and proportion of quarantined exposed individuals, showed negative index. The numbers indicate that an increase in the parameter value could decrease the disease’s endemicity. All in all, the study concludes that treatments for COVID-19 should focus on restriction of interaction between individuals and optimization of quarantine.

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Forward Bifurcation with Hysteresis Phenomena from Atherosclerosis Mathematical Model

Communication in Biomathematical Sciences ◽

10.5614/cbms.2021.4.2.4 ◽

2021 ◽

Vol 4 (2) ◽

pp. 125-137

Author(s):

Dipo Aldila ◽

Arthana Islamilova ◽

Sarbaz H.A. Khosnaw ◽

Bevina D. Handari ◽

Hengki Tasman

Keyword(s):

Mathematical Model ◽

Infection Rate ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Equilibrium Points ◽

Control Program ◽

Endemic Equilibrium ◽

Dynamic Complexity ◽

The Impact ◽

The Basic Reproduction Number

Atherosclerosis is a non-communicable disease (NCDs) which appears when the blood vessels in the human body become thick and stiff. The symptoms range from chest pain, sudden numbness in the arms or legs, temporary loss of vision in one eye, or even kidney failure, which may lead to death. Treatment in cases with severe symptoms requires surgery, in which the number of doctors or hospitals is limited in some countries, especially countries with low health levels. This article aims to propose a mathematical model to understand the impact of limited hospital resources on the success of the control program of atherosclerosis spreads. The model was constructed based on a deterministic model, where the hospitalization rate is defined as a time-dependent saturated function concerning the number of infected individuals. The existence and stability of all possible equilibrium points were shown analytically and numerically, along with the basic reproduction number. Our analysis indicates that our model may exhibit various types of bifurcation phenomena, such as forward bifurcation, backward bifurcation, or a forward bifurcation with hysteresis depending on the value of hospitalization saturation parameter and the infection rate for treated infected individuals. These phenomenon triggers a complex and tricky control program of atherosclerosis. A forward bifurcation with hysteresis auses a possible condition of having more than one stable endemic equilibrium when the basic reproduction number is larger than one, but close to one. The more significant value of hospitalization saturation rate or the infection rate for treated infected individuals increases the possibility of the stable endemic equilibrium point even though the disease-free equilibrium is stable. Furthermore, the Pontryagin Maximum Principle was used to characterize the optimal control problem for our model. Based on the results of our analysis, we conclude that atherosclerosis control interventions should prioritize prevention efforts over endemic reduction scenarios to avoid high intervention costs. In addition, the government also needs to pay great attention to the availability of hospital services for this disease to avoid the dynamic complexity of the spread of atherosclerosis in the field.

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