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.

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 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.

scholarly journals Stability Analysis and Optimal Control Strategy for Prevention of Pine Wilt Disease

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Kwang Sung Lee
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Control Strategies ◽  
Pine Wilt Disease ◽  
Wilt Disease ◽  
Pine Wilt ◽  
The Stability ◽  
The Basic Reproduction Number

We propose a mathematical model of pine wilt disease (PWD) which is caused by pine sawyer beetles carrying the pinewood nematode (PWN). We calculate the basic reproduction numberR0and investigate the stability of a disease-free and endemic equilibrium in a given mathematical model. We show that the stability of the equilibrium in the proposed model can be controlled through the basic reproduction numberR0. We then discuss effective optimal control strategies for the proposed PWD mathematical model. We demonstrate the existence of a control problem, and then we apply both analytical and numerical techniques to demonstrate effective control methods to prevent the transmission of the PWD. In order to do this, we apply two control strategies: tree-injection of nematicide and the eradication of adult beetles through aerial pesticide spraying. Optimal prevention strategies can be determined by solving the corresponding optimality system. Numerical simulations of the optimal control problem using a set of reasonable parameter values suggest that reducing the number of pine sawyer beetles is more effective than the tree-injection strategy for controlling the spread of PWD.

Optimal Control Analysis of a Cholera Epidemic Model

2019 ◽  
Vol 14 (01) ◽  
pp. 27-48 ◽  
Author(s):  
Prabir Panja
Keyword(s):  
Optimal Control ◽  
Vibrio Cholerae ◽  
Basic Reproduction Number ◽  
Disease Transmission ◽  
Human Population ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Control Analysis ◽  
Number Formula ◽  
The Basic Reproduction Number

In this paper, a cholera disease transmission mathematical model has been developed. According to the transmission mechanism of cholera disease, total human population has been classified into four subpopulations such as (i) Susceptible human, (ii) Exposed human, (iii) Infected human and (iv) Recovered human. Also, the total bacterial population has been classified into two subpopulations such as (i) Vibrio Cholerae that grows in the infected human intestine and (ii) Vibrio Cholerae in the environment. It is assumed that the cholera disease can be transmitted in a human population through the consumption of contaminated food and water by Vibrio Cholerae bacterium present in the environment. Also, it is assumed that Vibrio Cholerae bacterium is spread in the environment through the vomiting and feces of infected humans. Positivity and boundedness of solutions of our proposed system have been investigated. Equilibrium points and the basic reproduction number [Formula: see text] are evaluated. Local stability conditions of disease-free and endemic equilibrium points have been discussed. A sensitivity analysis has been carried out on the basic reproduction number [Formula: see text]. To eradicate cholera disease from the human population, an optimal control problem has been formulated and solved with the help of Pontryagin’s maximum principle. Here treatment, vaccination and awareness programs have been considered as control parameters to reduce the number of infected humans from cholera disease. Finally, the optimal control and the cost-effectiveness analysis of our proposed model have been performed numerically.

Dynamical Behavior of a Malaria Model with Discrete Delay and Optimal Insecticide Control

2017 ◽  
Vol 12 (01) ◽  
pp. 19-38 ◽  
Author(s):  
Tuhin Kumar Kar ◽  
Soovoojeet Jana
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Basic Reproduction Number ◽  
Human Population ◽  
Reproduction Number ◽  
Dynamical Behavior ◽  
Control Variable ◽  
Discrete Delay ◽  
Insecticide Control

In this paper we have proposed and analyzed a simple three-dimensional mathematical model related to malaria disease. We consider three state variables associated with susceptible human population, infected human population and infected mosquitoes, respectively. A discrete delay parameter has been incorporated to take account of the time of incubation period with infected mosquitoes. We consider the effect of insecticide control, which is applied to the mosquitoes. Basic reproduction number is figured out for the proposed model and it is shown that when this threshold is less than unity then the system moves to the disease-free state whereas for higher values other than unity, the system would tend to an endemic state. On the other hand if we consider the system with delay, then there may exist some cases where the endemic equilibrium would be unstable although the numerical value of basic reproduction number may be greater than one. We formulate and solve the optimal control problem by considering insecticide as the control variable. Optimal control problem assures to obtain better result than the noncontrol situation. Numerical illustrations are provided in support of the theoretical results.

A MODEL OF THE TRANSMISSION DYNAMICS OF LEISHMANIASIS

2011 ◽  
Vol 19 (02) ◽  
pp. 237-250 ◽  
Author(s):  
EPHRAIM O. AGYINGI ◽  
DAVID S. ROSS ◽  
KARTHIK BATHENA
Keyword(s):  
Global Attractor ◽  
Basic Reproduction Number ◽  
Human Population ◽  
Reproduction Number ◽  
Transmission Dynamics ◽  
Sis Model ◽  
Vector Population ◽  
Single Animal ◽  
Reservoir Hosts ◽  
The Basic Reproduction Number

In this paper we present a susceptible–infectious–susceptible (SIS) model that describes the transmission dynamics of cutaneous Leishmaniasis. The model treats a vector population and several populations of different mammals. Members of the human population serve as the incidental hosts, and members of the various animals populations serve as reservoir hosts. We establish the basic reproduction number and the equilibrium conditions of the system. We use a generalization of the Lyapunov function approach to show that when the basic reproduction number is less than or equal to one, the diseases-free equilibrium is a global attractor, and that when it is greater than one the endemic equilibrium is a global attractor. We present numerical simulations that demonstrate the dynamics of the model for a system containing a human population and a single animal population.

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.

scholarly journals Impact of Hygiene on Malaria Transmission Dynamics: A Mathematical Model

2021 ◽  
Author(s):  
Temidayo Oluwafemi ◽  
Emmanuel Azuaba
Keyword(s):  
Mathematical Model ◽  
Malaria Transmission ◽  
Basic Reproduction Number ◽  
Human Population ◽  
Reproduction Number ◽  
Model System ◽  
Transmission Dynamics ◽  
The Impact ◽  
Disease Free ◽  
The Basic Reproduction Number

Malaria continues to pose a major public health challenge, especially in developing countries, 219 million cases of malaria were estimated in 89 countries. In this paper, a mathematical model using non-linear differential equations is formulated to describe the impact of hygiene on Malaria transmission dynamics, the model is analyzed. The model is divided into seven compartments which includes five human compartments namely; Unhygienic susceptible human population, Hygienic Susceptible Human population, Unhygienic infected human population , hygienic infected human population and the Recovered Human population  and the mosquito population is subdivided into susceptible mosquitoes  and infected mosquitoes . The positivity of the solution shows that there exists a domain where the model is biologically meaningful and mathematically well-posed. The Disease-Free Equilibrium (DFE) point of the model is obtained, we compute the Basic Reproduction Number using the next generation method and established the condition for Local stability of the disease-free equilibrium, and we thereafter obtained the global stability of the disease-free equilibrium by constructing the Lyapunov function of the model system. Also, sensitivity analysis of the model system was carried out to identify the influence of the parameters on the Basic Reproduction Number, the result shows that the natural death rate of the mosquitoes is most sensitive to the basic reproduction number.

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).

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