EPIDEMIC SPREADING ON THREE-LAYER INTERDEPENDENT NETWORKS

2016 ◽  
Vol 24 (04) ◽  
pp. 469-494 ◽  
Author(s):  
LINGNA WANG ◽  
GUANGHU ZHU ◽  
HUIYAN KANG ◽  
XINCHU FU
Keyword(s):  
Infection Rate ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Mean Field ◽  
Network Size ◽  
Infection Rates ◽  
Epidemic Spreading ◽  
Interdependent Networks ◽  
Coupled Networks ◽  
The Basic Reproduction Number

Many epidemic diseases spread among three different populations with different contact patterns and infection rates. In response to such diseases, we propose two new types of three-layer interdependent networks — string-coupled networks and circular-coupled networks. We investigate an epidemic spreading on the two types of interdependent networks, propose two mathematical models through heterogeneous mean field approach and prove global stability of the disease-free and endemic equilibria. Through theoretical and numerical analysis, we find the following: the increase of each infection rate affects effectively only its own subnetwork and neighbors; in a string-coupled network, the middle subnetwork has bigger impact on the basic reproduction number than the end subnetworks with the growth of network size or infection rates; the basic reproduction number on a circular-coupled network is larger than that on a string-coupled network for a fixed network size; but the change of the basic reproduction number (or the average infection densities) is almost the same on both string-coupled and circular-coupled networks with the increasing of certain infection rate.

scholarly journals Forward Bifurcation with Hysteresis Phenomena from Atherosclerosis Mathematical Model

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.

scholarly journals Estimating the reproduction number of COVID-19 in Iran using epidemic modeling

2020 ◽  
Author(s):  
Ebrahim Sahafizadeh ◽  
Samaneh Sartoli
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Model ◽  
The Novel ◽  
Epidemic Spreading ◽  
Social Distancing ◽  
Novel Coronavirus ◽  
And Control ◽  
Second Wave ◽  
The Basic Reproduction Number

AbstractBackgroundAs reported by Iranian governments, the first cases of coronavirus (COVID-19) infections confirmed in Qom, Iran on February 19, 2020 (30 Bahman 1398). The number of identified cases afterward increased rapidly and the novel coronavirus spread to all provinces of the country. This study aimed to fit an epidemic model to the reported cases data to estimate the basic reproduction number (R0) of COVID-19 in Iran.MethodsWe used data from February 21, 2020, to April 21, 2020, on the number of cases reported by Iranian governments and we employed the SIR (Susceptible-Infectious-Removed) epidemic spreading model to fit the transmission model to the reported cases data by tuning the parameters in order to estimate the basic reproduction number of COVID-19 in Iran.ResultsThe value of reproduction number was estimated 4.86 in the first week and 4.5 in the second week. it decreased from 4.29 to 2.37 in the next four weeks. At the seventh week of the outbreak the reproduction number was reduced below one.ConclusionsThe results indicate that the basic reproduction number of COVID-19 was significantly larger than one in the early stages of the outbreak. However, implementing social distancing and preventing travelling on Nowruz (Persian New Year) effectively reduced the reproduction number. Although the results indicate that reproduction number is below one, it is necessary to continue social distancing and control travelling to prevent causing a second wave of outbreak.

scholarly journals First Consistent Determination of the Basic Reproduction Number for the First Covid-19 Wave in 71 Countries from the SIR-Epidemics Model with a Constant Ratio of Recovery to Infection Rate

2020 ◽  
pp. 37-43
Author(s):  
R. Schlickeiser ◽  
M. Kröger
Keyword(s):  
Infection Rate ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Simple Relation ◽  
Reproduction Numbers ◽  
Serial Interval ◽  
Reproduction Factor ◽  
Interval Distribution ◽  
The Basic Reproduction Number

The box-shaped serial interval distribution and the analytical solution of the Susceptible Infectious-Recovered (SIR)-epidemics model with a constant time-independent ratio of the recovery (μ0) to infection rate (a0) are used to calculate the effective reproduction factor and the basic reproduction number R0. The latter depends on the positively valued net infection number x = 13.5(a0 − μ0) as R0(x) = x(1 − e−x)−1 which for all values of x is greater unity. This dependence differs from the simple relation R0 = a0/μ0. With the earlier determination of the values of k and a0 of the Covid-19 pandemic waves in 71 countries the net infection rates and the basic reproduction numbers for these countries are calculated.

Optimal control for dengue eradication program under the media awareness effect

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Dipo Aldila
Keyword(s):  
Basic Reproduction Number ◽  
Death Rate ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Hospitalization Rate ◽  
Infection Rates ◽  
Control Variables ◽  
Eradication Program ◽  
The Media ◽  
The Basic Reproduction Number

Abstract In this article, a mathematical model is proposed to assess the effects of media awareness on dengue eradication programs. First, the existence and local stability of equilibrium points are discussed using the concept of the basic reproduction number. Using the center-manifold theorem, it is shown that the proposed model always undergoes a forward bifurcation at the basic reproduction number equal to unity. It is observed that the high-intensity media awareness could reduce the size of the endemic equilibrium. Based on local sensitivity analysis, we identify the three most sensitive parameters, namely the natural death rate of mosquito (μ v ), infection rates (β h1, β v1), and hospitalization rate (η). Hence, control variables need to be introduced to increase/reduce these parameters. In this article, we use three different control variables, namely the media campaign, (u 1(t)), to reduce infection rates, additional hospitalization rate, (u 2(t)), and fumigation rate, (u 3(t)), to increase mosquitoes death rate. Pontryagin’s maximum principle is used to determine the optimal conditions. Some numerical simulations are performed to describe a possible scenario in the field. Cost effectiveness analysis is then conducted to determine the best strategy for the dengue eradication program. We conclude that a combination of media campaigns and fumigation is the most effective strategy to prevent a significant increase in the number of infected individuals.

scholarly journals Fractional SIR-Model for Estimating Transmission Dynamics of COVID-19 in India

J ◽  
2021 ◽  
Vol 4 (2) ◽  
pp. 86-100
Author(s):  
Nita H. Shah ◽  
Ankush H. Suthar ◽  
Ekta N. Jayswal ◽  
Ankit Sikarwar
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Sir Model ◽  
Time Dependent ◽  
Contact Rate ◽  
Distribution Maps ◽  
Fundamental Parameters ◽  
Different Order ◽  
The Basic Reproduction Number

In this article, a time-dependent susceptible-infected-recovered (SIR) model is constructed to investigate the transmission rate of COVID-19 in various regions of India. The model included the fundamental parameters on which the transmission rate of the infection is dependent, like the population density, contact rate, recovery rate, and intensity of the infection in the respective region. Looking at the great diversity in different geographic locations in India, we determined to calculate the basic reproduction number for all Indian districts based on the COVID-19 data till 7 July 2020. By preparing district-wise spatial distribution maps with the help of ArcGIS 10.2, the model was employed to show the effect of complete lockdown on the transmission rate of the COVID-19 infection in Indian districts. Moreover, with the model's transformation to the fractional ordered dynamical system, we found that the nature of the proposed SIR model is different for the different order of the systems. The sensitivity analysis of the basic reproduction number is done graphically which forecasts the change in the transmission rate of COVID-19 infection with change in different parameters. In the numerical simulation section, oscillations and variations in the model compartments are shown for two different situations, with and without lockdown.

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

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.

scholarly journals Mathematical analysis of a measles transmission dynamics model in Bangladesh with double dose vaccination

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Md Abdul Kuddus ◽  
M. Mohiuddin ◽  
Azizur Rahman
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Equilibrium Points ◽  
Rank Correlation ◽  
Dynamical Analysis ◽  
Model Parameters ◽  
Progression Rate ◽  
Double Dose ◽  
The Basic Reproduction Number

AbstractAlthough the availability of the measles vaccine, it is still epidemic in many countries globally, including Bangladesh. Eradication of measles needs to keep the basic reproduction number less than one $$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{R}}_{0}<1)$$ ( i . e . R 0 < 1 ) . This paper investigates a modified (SVEIR) measles compartmental model with double dose vaccination in Bangladesh to simulate the measles prevalence. We perform a dynamical analysis of the resulting system and find that the model contains two equilibrium points: a disease-free equilibrium and an endemic equilibrium. The disease will be died out if the basic reproduction number is less than one $$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{ R}}_{0}<1)$$ ( i . e . R 0 < 1 ) , and if greater than one $$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{R}}_{0}>1)$$ ( i . e . R 0 > 1 ) epidemic occurs. While using the Routh-Hurwitz criteria, the equilibria are found to be locally asymptotically stable under the former condition on $${\mathrm{R}}_{0}$$ R 0 . The partial rank correlation coefficients (PRCCs), a global sensitivity analysis method is used to compute $${\mathrm{R}}_{0}$$ R 0 and measles prevalence $$\left({\mathrm{I}}^{*}\right)$$ I ∗ with respect to the estimated and fitted model parameters. We found that the transmission rate $$(\upbeta )$$ ( β ) had the most significant influence on measles prevalence. Numerical simulations were carried out to commissions our analytical outcomes. These findings show that how progression rate, transmission rate and double dose vaccination rate affect the dynamics of measles prevalence. The information that we generate from this study may help government and public health professionals in making strategies to deal with the omissions of a measles outbreak and thus control and prevent an epidemic in Bangladesh.

scholarly journals Mathematical analysis of a within-host model of SARS-CoV-2

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Bhagya Jyoti Nath ◽  
Kaushik Dehingia ◽  
Vishnu Narayan Mishra ◽  
Yu-Ming Chu ◽  
Hemanta Kumar Sarmah
Keyword(s):  
Stability Analysis ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Basic Reproduction Ratio ◽  
Viral Kinetics ◽  
Reproduction Ratio ◽  
Biological Implication ◽  
Infection Models ◽  
Kinetics Of ◽  
The Basic Reproduction Number

AbstractIn this paper, we have mathematically analyzed a within-host model of SARS-CoV-2 which is used by Li et al. in the paper “The within-host viral kinetics of SARS-CoV-2” published in (Math. Biosci. Eng. 17(4):2853–2861, 2020). Important properties of the model, like nonnegativity of solutions and their boundedness, are established. Also, we have calculated the basic reproduction number which is an important parameter in the infection models. From stability analysis of the model, it is found that stability of the biologically feasible steady states are determined by the basic reproduction number $(\chi _{0})$ ( χ 0 ) . Numerical simulations are done in order to substantiate analytical results. A biological implication from this study is that a COVID-19 patient with less than one basic reproduction ratio can automatically recover from the infection.

Sign in / Sign up

Export Citation Format

Share Document