scholarly journals Comparison of smallpox outbreak control strategies using a spatial metapopulation model

2007 ◽  
Vol 135 (7) ◽  
pp. 1133-1144 ◽  
Author(s):  
I. M. HALL ◽  
J. R. EGAN ◽  
I. BARRASS ◽  
R. GANI ◽  
S. LEACH
Keyword(s):  
Great Britain ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Control Strategies ◽  
Mass Vaccination ◽  
Metapopulation Model ◽  
Reproduction Numbers ◽  
Potential Benefits ◽  
Index Cases ◽  
The Basic Reproduction Number

SUMMARYTo determine the potential benefits of regionally targeted mass vaccination as an adjunct to other smallpox control strategies we employed a spatial metapopulation patch model based on the administrative districts of Great Britain. We counted deaths due to smallpox and to vaccination to identify strategies that minimized total deaths. Results confirm that case isolation, and the tracing, vaccination and observation of case contacts can be optimal for control but only for optimistic assumptions concerning, for example, the basic reproduction number for smallpox (R0=3) and smaller numbers of index cases (∼10). For a wider range of scenarios, including larger numbers of index cases and higher reproduction numbers, the addition of mass vaccination targeted only to infected districts provided an appreciable benefit (5–80% fewer deaths depending on where the outbreak started with a trigger value of 1–10 isolated symptomatic individuals within a district).

scholarly journals Optimal Control of a Dengue-Dengvaxia Model: Comparison Between Vaccination and Vector Control

2021 ◽  
Vol 9 (1) ◽  
pp. 198-212
Author(s):  
Cheryl Q. Mentuda
Keyword(s):  
Optimal Control ◽  
Vector Control ◽  
Basic Reproduction Number ◽  
Human Population ◽  
Model Comparison ◽  
Reproduction Number ◽  
Control Strategies ◽  
Minimum Principle ◽  
Transmitted Disease ◽  
The Basic Reproduction Number

Abstract Dengue is the most common mosquito-borne viral infection transmitted disease. It is due to the four types of viruses (DENV-1, DENV-2, DENV-3, DENV-4), which transmit through the bite of infected Aedes aegypti and Aedes albopictus female mosquitoes during the daytime. The first globally commercialized vaccine is Dengvaxia, also known as the CYD-TDV vaccine, manufactured by Sanofi Pasteur. This paper presents a Ross-type epidemic model to describe the vaccine interaction between humans and mosquitoes using an entomological mosquito growth population and constant human population. After establishing the basic reproduction number ℛ0, we present three control strategies: vaccination, vector control, and the combination of vaccination and vector control. We use Pontryagin’s minimum principle to characterize optimal control and apply numerical simulations to determine which strategies best suit each compartment. Results show that vector control requires shorter time applications in minimizing mosquito populations. Whereas vaccinating the primary susceptible human population requires a shorter time compared to the secondary susceptible human.

scholarly journals Dynamics Analysis of a Viral Infection Model with a General Standard Incidence Rate

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Yu Ji ◽  
Muxuan Zheng
Keyword(s):  
Viral Infection ◽  
Incidence Rate ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Infection Model ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Reproduction Numbers ◽  
The Basic Reproduction Number ◽  
General Standard

The basic viral infection models, proposed by Nowak et al. and Perelson et al., respectively, have been widely used to describe viral infection such as HBV and HIV infection. However, the basic reproduction numbers of the two models are proportional to the number of total cells of the host's organ prior to the infection, which seems not to be reasonable. In this paper, we formulate an amended model with a general standard incidence rate. The basic reproduction number of the amended model is independent of total cells of the host’s organ. When the basic reproduction numberR0<1, the infection-free equilibrium is globally asymptotically stable and the virus is cleared. Moreover, ifR0>1, then the endemic equilibrium is globally asymptotically stable and the virus persists in the host.

GLOBAL ANALYSIS OF A VIRAL INFECTION MODEL WITH APPLICATION TO HBV INFECTION

2010 ◽  
Vol 18 (02) ◽  
pp. 325-337 ◽  
Author(s):  
YU JI ◽  
LEQUAN MIN ◽  
YONGAN YE
Keyword(s):  
Viral Infection ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Global Analysis ◽  
Hiv Infections ◽  
Hbv Infection ◽  
Infection Model ◽  
Globally Asymptotically Stable ◽  
Reproduction Numbers ◽  
The Basic Reproduction Number

The basic models of within-host viral infection, proposed by Nowak and May2 and Perelson and Nelson,5 have been widely used in the studies of HBV and HIV infections. The basic reproduction numbers of the two models are proportional to the number of total cells of the host's organ prior to the infection. In this paper, we formulate an amended Perelson and Nelson's model with standard incidence. The basic reproduction number of the amended model is independent of total cells of the host's organ. If the basic reproduction number R0 < 1, then the infection-free equilibrium is globally asymptotically stable and the virus is cleared; if R0 > 1, then the virus persists in the host, and solutions approach either an endemic equilibrium or a periodic orbit. Numerical simulations of this model agree well with the clinical HBV infection data. This can provide a possible interpretation for the viral oscillation behaviors, which were observed in chronic HBV infection patients.

scholarly journals Model matematika penyebaran COVID-19 dengan penggunaan masker kesehatan dan karantina

2021 ◽  
Vol 2 (2) ◽  
pp. 68-79
Author(s):  
Muhammad Manaqib ◽  
Irma Fauziah ◽  
Eti Hartati
Keyword(s):  
Numerical Simulations ◽  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Endemic Equilibrium ◽  
Reproduction Numbers ◽  
Geometric Picture ◽  
Disease Free ◽  
The Basic Reproduction Number

This study developed a model for the spread of COVID-19 disease using the SIR model which was added by a health mask and quarantine for infected individuals. The population is divided into six subpopulations, namely the subpopulation susceptible without a health mask, susceptible using a health mask, infected without using a health mask, infected using a health mask, quarantine for infected individuals, and the subpopulation to recover. The results obtained two equilibrium points, namely the disease-free equilibrium point and the endemic equilibrium point, and the basic reproduction number (R0). The existence of a disease-free equilibrium point is unconditional, whereas an endemic equilibrium point exists if the basic reproduction number is more than one. Stability analysis of the local asymptotically stable disease-free equilibrium point when the basic reproduction number is less than one. Furthermore, numerical simulations are carried out to provide a geometric picture related to the results that have been analyzed. The results of numerical simulations support the results of the analysis obtained. Finally, the sensitivity analysis of the basic reproduction numbers carried out obtained four parameters that dominantly affect the basic reproduction number, namely the rate of contact of susceptible individuals with infection, the rate of health mask use, the rate of health mask release, and the rate of quarantine for infected individuals.

OPTIMAL CONTROL ANALYSIS OF THE EFFECT OF TREATMENT, ISOLATION AND VACCINATION ON HEPATITIS B VIRUS

2020 ◽  
Vol 28 (02) ◽  
pp. 351-376 ◽  
Author(s):  
MUHAMMAD ALTAF KHAN ◽  
SYED AZHAR ALI SHAH ◽  
SAIF ULLAH ◽  
KAZEEM OARE OKOSUN ◽  
MUHAMMAD FAROOQ
Keyword(s):  
Optimal Control ◽  
Hepatitis B ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Control Strategies ◽  
Control Measures ◽  
Hepatitis B Infection ◽  
Control Variables ◽  
Effect Of Treatment ◽  
The Basic Reproduction Number

Hepatitis B infection is a serious health issue and a major cause of deaths worldwide. This infection can be overcome by adopting proper treatment and control strategies. In this paper, we develop and use a mathematical model to explore the effect of treatment on the dynamics of hepatitis B infection. First, we formulate and use a model without control variables to calculate the basic reproduction number and to investigate basic properties of the model such as the existence and stability of equilibria. In the absence of control measures, we prove that the disease free equilibrium is locally asymptotically stable when the basic reproduction number is less than unity. Also, using persistent theorem, it is shown that the infection is uniformly persistent, whenever the basic reproduction number is greater than unity. Using optimal control theory, we incorporate into the model three time-dependent control variables and investigate the conditions required to curtail the spread of the disease. Finally, to illustrate the effectiveness of each of the control strategies on disease control and eradication, we perform numerical simulations. Based on the numerical results, we found that the first two strategies (treatment and isolation strategy) and (vaccination and isolation strategy) are not very effective as a long term control or eradication strategy for HBV. Hence, we recommend that in order to effectively control the disease, all the control measures (isolation, vaccination and treatment) must be implemented at the same time.

scholarly journals The long-term dynamics of tuberculosis and other diseases with long serial intervals: implications of and for changing reproduction numbers

1998 ◽  
Vol 121 (2) ◽  
pp. 309-324 ◽  
Author(s):  
E. VYNNYCKY ◽  
P. E. M. FINE
Keyword(s):  
Infectious Disease ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
England And Wales ◽  
Transmission Potential ◽  
Reproduction Numbers ◽  
Serial Interval ◽  
Net Reproduction ◽  
Epidemiological Parameters ◽  
The Basic Reproduction Number

The net and basic reproduction numbers are among the most widely-applied concepts in infectious disease epidemiology. A net reproduction number (the average number of secondary infectious cases resulting from each case in a given population) of above 1 is conventionally associated with an increase in incidence; the basic reproduction number (defined analogously for a ‘totally susceptible’ population) provides a standard measure of the ‘transmission potential’ of an infection. Using a model of the epidemiology of tuberculosis in England and Wales since 1900, we demonstrate that these measures are difficult to apply if disease can follow reinfection, and that they lose their conventional interpretations if important epidemiological parameters, such as the rate of contact between individuals, change over the time interval between successive cases in a chain of transmission (the serial interval).The net reproduction number for tuberculosis in England and Wales appears to have been approximately 1 from 1900 until 1950, despite concurrent declines in morbidity and mortality rates, and it declined rapidly in the second half of this century. The basic reproduction number declined from about 3 in 1900, reached 2 by 1950, and first fell below 1 in about 1960. Reductions in effective contact between individuals over this period, measured in terms of the average number of individuals to whom each case could transmit the infection, meant that the conventional basic reproduction number measure (which does not consider subsequent changes in epidemiological parameters) for a given year failed to reflect the ‘actual transmission potential’ of the infection. This latter property is better described by a variant of the conventional measure which takes secular trends in contact into account. These results are relevant for the interpretation of trends in any infectious disease for which epidemiological parameters change over time periods comparable to the infectious period, incubation period or serial interval.

scholarly journals SEIITR Model for Diabetes Mellitus Distribution in Case of Insulin and Care Factors

2020 ◽  
Vol 5 (2) ◽  
pp. 100-106
Author(s):  
Nur Fajri ◽  
Sanusi ◽  
Asmaidi
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Fixed Point ◽  
Fixed Points ◽  
Basic Reproduction Number ◽  
Human Population ◽  
Reproduction Number ◽  
Model Type ◽  
Reproduction Numbers ◽  
The Basic Reproduction Number

This research is done to learn diabetes mellitus type SEIITR with insulin and care factors. Mathematical model type SEIITR is a mathematical model of diabetes in which the human population is divided into five groups: susceptible humans (Susceptible) S, exposed (Exposed) E, infected I without treatment, infected (Infected) IT  with treatment dan recovered (Recovery) R. The SEIITR model has two fixed points, namely, a fixed point without disease and an endemic fixed point. By using basic reproduction numbers (R0), it is found that the fixed point without disease is stable if R0 < 1 and when R0 > 1. Then the fixed point without disease is unstable. The simulation shows the effect of giving insulin to changes in the value of the basic reproduction number. If the effectiveness of β decreases, the basic reproduction number decreases too. Thus, a decrease in the value of this parameter will be able to help reduce the rate of diabetes mellitus in the population.

scholarly journals Implications of the COVID-19 pandemic on eliminating trachoma as a public health problem

2020 ◽  
Author(s):  
Seth Blumberg ◽  
Anna Borlase ◽  
Joaquin M Prada ◽  
Anthony W Solomon ◽  
Paul Emerson ◽  
...  
Keyword(s):  
Public Health ◽  
Basic Reproduction Number ◽  
Health Problem ◽  
Reproduction Number ◽  
Control Strategies ◽  
Public Health Problem ◽  
New Paradigm ◽  
Specific Implementation ◽  
The Impact ◽  
The Basic Reproduction Number

AbstractBackgroundProgress towards elimination of trachoma as a public health problem has been substantial, but the COVID-19 pandemic has disrupted community-based control efforts.MethodsWe use a susceptible-infected model to estimate the impact of delayed distribution of azithromycin treatment on the prevalence of active trachoma.ResultsWe identify three distinct scenarios for geographic districts depending on whether the basic reproduction number and the treatment-associated reproduction number are above or below a value of one. We find that when the basic reproduction number is below one, no significant delays in disease control will be caused. However, when the basic reproduction number is above one, significant delays can occur. In most districts a year of COVID-related delay can be mitigated by a single extra round of mass drug administration. However, supercritical districts require a new paradigm of infection control because the current strategies will not eliminate disease.ConclusionIf the pandemic can motivate judicious, community-specific implementation of control strategies, global elimination of trachoma as a public health problem could be accelerated.

Theoretical assessment of the impact of environmental contamination on the dynamical transmission of polio

2019 ◽  
Vol 12 (02) ◽  
pp. 1950012 ◽  
Author(s):  
C. Balde ◽  
M. Lam ◽  
A. Bah ◽  
S. Bowong ◽  
J. J. Tewa
Keyword(s):  
Basic Reproduction Number ◽  
Environmental Contamination ◽  
Reproduction Number ◽  
Control Strategies ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Indirect Transmission ◽  
Populations At Risk ◽  
The Impact ◽  
The Basic Reproduction Number

A mathematical model for the dynamical transmission of polio is considered, with the aim of investigating the impact of environment contamination. The model captures two infection pathways through both direct human-to-human transmission and indirect human-to-environment-to-human transmission by incorporating the environment as a transition and/or reservoir of viruses. We derive the basic reproduction number [Formula: see text]. We show that the disease free equilibrium is globally asymptotically stable (GAS) if [Formula: see text], while if [Formula: see text], there exists a unique endemic equilibrium which is locally asymptotically stable (LAS). Similar results hold for environmental contamination free sub-model (without the incorporation of the indirect transmission). At the endemic level, we show that the number of infected individuals for the model with the environmental-related contagion is greater than the corresponding number for the environmental contamination free sub-model. In conjunction with the inequality [Formula: see text], where [Formula: see text] is the basic reproduction number for the environmental contamination free sub-model, our finding suggests that the contaminated environment plays a detrimental role on the transmission dynamics of polio disease by increasing the endemic level and the severity of the outbreak. Therefore, it is natural to implement control strategies to reduce the severity of the disease by providing adequate hygienic living conditions, educate populations at risk to follow rigorously those basic hygienic rules in order to avoid adequate contacts with suspected contaminated objects. Further, we perform numerical simulations to support the theory.

scholarly journals Modelling the Periodic Outbreak of Measles in Mainland China

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Yuyi Xue ◽  
Xiaoe Ruan ◽  
Yanni Xiao
Keyword(s):  
Optimal Control ◽  
Numerical Simulations ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Control Strategies ◽  
Mainland China ◽  
Asymptomatic Infection ◽  
Protection Measures ◽  
The Basic Reproduction Number

In mainland China, measles infection reached the lowest level in 2012 but resurged again after that with a seasonally fluctuating pattern. To investigate the phenomenon of periodic outbreak and identify the crucial parameters that play in the transmission dynamics of measles, we formulate a mathematical model incorporating periodic transmission rate and asymptomatic infection with waning immunity. We define the basic reproduction number as the threshold value to govern whether measles infection dies out or not. Fitting the reported measles cases from 2013 to 2016 to our proposed model, we estimate the basic reproduction number R0 with immunization to be 1.0077. From numerical simulations, we conclude asymptomatic infection does not cause much new infections and the key parameters affecting the transmission of measles are vaccination rate, transmission rate, and recovery rate, which suggests the public to enhance vaccination and protection measures to reduce effective contacts between susceptible and infective individuals and treat infected individuals timely. To minimize the number of infected individuals at a minimal cost, we formulate an optimal control system to design optimal control strategies. Numerical simulations show the effectiveness of optimal control strategies and recommend us to implement the control strategies as soon as possible. In particular, enhancing vaccination is especially effective in lowering the initial outbreak and making disease recurrence less likely.

Sign in / Sign up

Export Citation Format

Share Document