PEMODELAN MATEMATIKA TERHADAP PENYEBARAN VIRUS KOMPUTER DENGAN PROBABILITAS KEKEBALAN

The increase in the number of computer viruses can be modeled with a mathematical model of the spread of SEIR type of diseases with immunity probability. This study aims to model the pattern of the spread of computer viruses. The method used in this research is the analytical method with the probability of mathematical immunity. Based on the analysis of the model, two equilibrium points free from disease E1 and endemic equilibrium points E2 were obtained. The existence and local stability of the equilibrium point depends on the basic reproduction number R0. Equilibrium points E1 and E2 tend to be locally stable because R0<1 which means there is no spread of disease. While the numerical simulation results shown that the size of the probability of immunity will affect compartment R and the minimum size of a new computer and the spread of computer viruses will affect compartments S and E on the graph of the simulation results. The conclusion obtained by the immune model SEIR successfully shows that increasing the probability of immunity significantly affects the increase in the number of computer hygiene after being exposed to a virus.

Download Full-text

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.

Download Full-text

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

Download Full-text

ANALISIS KESTABILAN MODEL PENYEBARAN PENYAKIT TUBERKULOSIS DENGAN LAJU INFEKSI TERSATURASI (STABILITY ANALYSIS OF TUBERCOLOSIS SPREAD DISEASES MODEL CONSIDERING SATURATED INFECTION RATE)

Jurnal Matematika Thales ◽

10.22146/jmt.51490 ◽

2020 ◽

Vol 2 (1) ◽

Author(s):

Handika Lintang Saputra ◽

Sutimin Sutimin ◽

Sutrisno Sutrisno

Keyword(s):

Equilibrium Point ◽

Local Stability ◽

Stability Property ◽

Reproduction Number ◽

Equilibrium Points ◽

Dynamical Behavior ◽

Asymptotically Stable ◽

Simulation Results ◽

Tuberculosis Disease ◽

The Basic Reproduction Number

This paper deals with the analysis of tuberculosis disease spread model with saturated infection rate and the treatment effect. We analyze the dynamical behavior of the model to observe the stability peroperty of the model’s equilibrium points. The Routh-Hurwitz Theorem is used to analyze the local stability peroperty of the free disease equilibrium point whereas Transcritical Bifurcation principle is used to analyze the local stability property of the endemic equilibrium pont. The result show that the local stability property of the equilibrium points is depending on the basic reproduction number value calculated by the next generation matrix (NGM). When the basic reproduction number is less than 1, the free disease equilibrium point is locally asymptotically stable, and when it is greater than 1, the endemic equilibrium point is locally asymptotically stable. Numeric simulation results were presented to describe the evolution of the dynamical behavior and to understand the treatment effectiveness for the tuberculosis disease of the population. From the simulation results, it was derived that the treatment in the infected subpopulation had a better result than the one in latent.

Download Full-text

Mathematical Assessment of the Dynamical Model of Smoking Tobacco Epidemic in Bangladesh

International Journal of Science and Management Studies (IJSMS) ◽

10.51386/25815946/ijsms-v3i2p105 ◽

2020 ◽

pp. 36-48

Author(s):

Sk. Abdus Samad ◽

Md. Tusberul Islam ◽

Sayed Toufiq Hossain Tomal ◽

MHA Biswas

Keyword(s):

Numerical Simulation ◽

Mathematical Model ◽

Stability Analysis ◽

Differential Equations ◽

Basic Reproduction Number ◽

Conversion Rate ◽

Reproduction Number ◽

The World ◽

Tobacco Epidemic ◽

The Basic Reproduction Number

Bangladesh is one of the largest tobacco users in the world being troubled by smoking related issues. In this paper we consider a compartmental mathematical model of smoking in which the population is divided into five compartments: susceptible, expose, smokers, temporary quitters and permanent quitters described by ordinary differential equations. We study by including the conversion rate from light smoker to permanent quit smokers. The basic reproduction number R0 has been derived and then we found two euilibria of the model one of them is smoking-free and other of them is smoking-present. We establish the positivity, boundedness of the solutions and perform stability analysis of the model. To decrease the smoking propensity in Bangladesh we perform numerical simulation for various estimations of parameters which offer understanding to give up smoking and how they influence the smoker and exposed class. This model gives us legitimate thought regarding the explanations for the spread of smoking in Bangladesh.

Download Full-text

Kestabilan Model Epidemi Seir dengan Matriks Hurwitz

Jurnal Ilmiah Poli Rekayasa ◽

10.30630/jipr.11.2.76 ◽

2016 ◽

Vol 11 (2) ◽

pp. 74

Author(s):

Roni Tri Putra ◽

Sukatik - ◽

Sri Nita

Keyword(s):

Basic Reproduction Number ◽

Epidemic Model ◽

Local Stability ◽

Reproduction Number ◽

Equilibrium Points ◽

Asymptotically Stable ◽

Stability Of Equilibrium ◽

Disease Free ◽

The Basic Reproduction Number

In this paper, it will be studied local stability of equilibrium points of a SEIR epidemic model with infectious force in latent, infected and immune period. From the model it will be found investigated the existence and its stability of points its equilibrium by Hurwitz matrices. The local stability of equilibrium points is depending on the value of the basic reproduction number If the disease free equilibrium is local asymptotically stable.

Download Full-text

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.

Download Full-text

Pemodelan Matematika SEIRS Pada Penyebaran Penyakit Malaria di Kabupaten Mimika

Journal of Mathematics, Computations, and Statistics ◽

10.35580/jmathcos.v4i1.20446 ◽

2021 ◽

Vol 4 (1) ◽

pp. 21

Author(s):

Hisyam Ihsan ◽

Syafruddin Side ◽

Musdalifa Pagga

Keyword(s):

Mathematical Model ◽

Equilibrium Point ◽

Basic Reproduction Number ◽

Reproduction Number ◽

District Health Office ◽

District Health ◽

Simulation Results ◽

The Mathematical Model ◽

Malaria Model ◽

The Basic Reproduction Number

Abstrak. Penelitian ini bertujuan untuk membangun model penyebaran pada penyakit malaria tipe SEIRS (Susceptible-Exposed- Infected- Recovered- Susceptible) dengan menambahkan parameter penanganan(pengobatan) pada kelas Exposed dan asumsi bahwa manusia yang pulih dapat rentan kembali terkena penyakit malaria. Model ini dibagi menjadi empat kelas yaitu, rentan, terinfeksi tapi belum aktif, terinfeksi, dan sembuh. Data yang digunakan adalah data jumlah penderita penyakit malaria dari Dinas Kesehatan Kabupaten Mimika tahun 2018. Model matematika tipe SEIRS digunakan untuk menentukan titik equilibrium. Berdasarkan hasil simulasi dari model SEIRS diperoleh bilangan reproduksi dasar sebesar 0,09 yang menandakan bahwa penyebaran penyakit malaria tidak menyebabkan orang lain terkena penyakit malaria.Kata Kunci: Titik Equilibrium, Bilangan Reproduksi Dasar, Malaria, Model SEIRSAbstract. This research aims to build a model of the spread of malaria diseases type SEIRS (Susceptible-Exposed-Infected-Recovered-Susceptible) by adding treatment parameters (treatment) in the Exposed class and the assumption that humans who recover can be vulnerable to malaria again. This model is divided into four classes namely, vulnerable, infected but not yet active, infected, and cured. The data used are data on the number of malaria sufferers from the Mimika District Health Office in 2018. The mathematical model of the type SEIRS is used to determine the equilibrium point. Based on the simulation results of the SEIRS model, the basic reproduction number (R0) of 0.09 indicates that the spread of malaria does not cause others to contract malaria.Keywords: Equilibrium Point, Basic Reproductive Numbers, Malaria, SEIRS Model

Download Full-text

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.

Download Full-text

Mathematical Modeling of Japanese Encephalitis under Aquatic Environmental Effects

Mathematics ◽

10.3390/math8111880 ◽

2020 ◽

Vol 8 (11) ◽

pp. 1880

Author(s):

Faïçal Ndaïrou ◽

Iván Area ◽

Delfim F. M. Torres

Keyword(s):

Mathematical Modeling ◽

Mathematical Model ◽

Japanese Encephalitis ◽

Environmental Effects ◽

Basic Reproduction Number ◽

Local Stability ◽

Reproduction Number ◽

Well Posed ◽

Disease Free ◽

The Basic Reproduction Number

We propose a mathematical model for the spread of Japanese encephalitis with emphasis on the environmental effects on the aquatic phase of mosquitoes. The model is shown to be biologically well-posed and to have a biologically and ecologically meaningful disease-free equilibrium point. Local stability is analyzed in terms of the basic reproduction number and numerical simulations presented and discussed.

Download Full-text

Impact of early detection and vaccination strategy in COVID-19 eradication program in Jakarta, Indonesia

BMC Research Notes ◽

10.1186/s13104-021-05540-9 ◽

2021 ◽

Vol 14 (1) ◽

Author(s):

Dipo Aldila ◽

Brenda M. Samiadji ◽

Gracia M. Simorangkir ◽

Sarbaz H. A. Khosnaw ◽

Muhammad Shahzad

Keyword(s):

Mathematical Model ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Vaccination Strategy ◽

Vaccination Rate ◽

Rapid Testing ◽

Social Distancing ◽

Rapid Spread ◽

Vaccine Potential ◽

The Basic Reproduction Number

Abstract Objective Several essential factors have played a crucial role in the spreading mechanism of COVID-19 (Coronavirus disease 2019) in the human population. These factors include undetected cases, asymptomatic cases, and several non-pharmaceutical interventions. Because of the rapid spread of COVID-19 worldwide, understanding the significance of these factors is crucial in determining whether COVID-19 will be eradicated or persist in the population. Hence, in this study, we establish a new mathematical model to predict the spread of COVID-19 considering mentioned factors. Results Infection detection and vaccination have the potential to eradicate COVID-19 from Jakarta. From the sensitivity analysis, we find that rapid testing is crucial in reducing the basic reproduction number when COVID-19 is endemic in the population rather than contact trace. Furthermore, our results indicate that a vaccination strategy has the potential to relax social distancing rules, while maintaining the basic reproduction number at the minimum possible, and also eradicate COVID-19 from the population with a higher vaccination rate. In conclusion, our model proposed a mathematical model that can be used by Jakarta’s government to relax social distancing policy by relying on future COVID-19 vaccine potential.

Download Full-text