scholarly journals On the Role of Short-Term Animal Movements on the Persistence of Brucellosis

Mathematics ◽  
2018 ◽  
Vol 6 (9) ◽  
pp. 154 ◽  
Author(s):  
Paride Lolika ◽  
Steady Mushayabasa
Keyword(s):  
Optimal Control ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Short Term ◽  
Optimal Control Strategy ◽  
Animal Movements ◽  
Zoonotic Infections ◽  
Integral Role ◽  
And Control ◽  
The Basic Reproduction Number

Short-term animal movements play an integral role in the transmission and control of zoonotic infections such as brucellosis, in communal farming zones where animal movements are highly uncontrolled. Such movements need to be incorporated in models that aim at informing animal managers effective ways to control the spread of zoonotic diseases. We developed, analyzed and simulated a two-patch mathematical model for brucellosis transmission that incorporates short-term animal mobility. We computed the basic reproduction number and demonstrated that it is a sharp threshold for disease dynamics. In particular, we demonstrated that, when the basic reproduction number is less than unity, then the disease dies out. However, if the basic reproduction number is greater than unity, the disease persists. Meanwhile, we applied optimal control theory to the proposed model with the aim of exploring the cost-effectiveness of different culling strategies. The results demonstrate that animal mobility plays an important role in shaping optimal control strategy.

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

Filomat ◽  
2019 ◽  
Vol 33 (17) ◽  
pp. 5691-5711 ◽  
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.

scholarly journals Sustainable social distancing through facemask use and testing during the Covid-19 pandemic

2020 ◽  
Author(s):  
Diego Chowell ◽  
Kimberlyn Roosa ◽  
Ranu Dhillon ◽  
Gerardo Chowell ◽  
Devabhaktuni Srikrishna
Keyword(s):  
Basic Reproduction Number ◽  
Symptom Onset ◽  
Social Protection ◽  
Reproduction Number ◽  
Type Model ◽  
Protective Behaviors ◽  
Social Distancing ◽  
And Control ◽  
Different Levels ◽  
The Basic Reproduction Number

We investigate how individual protective behaviors, different levels of testing, and isolation influence the transmission and control of the COVID-19 pandemic. Based on an SEIR-type model incorporating asymptomatic but infectious individuals (40%), we show that the pandemic may be readily controllable through a combination of testing, treatment if necessary, and self-isolation after testing positive (TTI) of symptomatic individuals together with social protection (e.g., facemask use, handwashing). When the basic reproduction number, R0, is 2.4, 65% effective social protection alone (35% of the unprotected transmission) brings the R below 1. Alternatively, 20% effective social protection brings the reproduction number below 1.0 so long as 75% of the symptomatic population is covered by TTI within 12 hours of symptom onset. Even with 20% effective social protection, TTI of 1 in 4 symptomatic individuals can substantially 'flatten the curve' cutting the peak daily incidence in half.

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 Estimation of Hospital Potential Capacity and Basic Reproduction Number

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Fei Wang ◽  
Linhua Wang ◽  
Peng Wang
Keyword(s):  
Infectious Disease ◽  
Decision Making ◽  
Resource Allocation ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Medical Resource ◽  
Population Dynamic Model ◽  
Potential Capacity ◽  
And Control ◽  
The Basic Reproduction Number

In order to reflect the population covered by institutional medical services, the concept of hospital potential capacity is proposed and a formula for its estimation is developed based on a population dynamic model. Using the collected data on hospital outpatient and inpatient services and the demographical information on Chongqing as an example, the demand for medical resource allocation in Chongqing is dynamically estimated. Moreover, the proposed formula is also useful in the estimation of the basic reproduction number in epidemiology. The results can be contributed to the improvement of decision-making in the allocation of medical resources and the evaluation of the interventions and control efforts of the infectious disease.

scholarly journals On an SE(Is)(Ih)AR epidemic model with combined vaccination and antiviral controls for COVID-19 pandemic

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
M. De la Sen ◽  
A. Ibeas
Keyword(s):  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Antiviral Treatment ◽  
Stability Properties ◽  
Local Asymptotic Stability ◽  
Proposed Model ◽  
And Control ◽  
The Basic Reproduction Number

AbstractIn this paper, we study the nonnegativity and stability properties of the solutions of a newly proposed extended SEIR epidemic model, the so-called SE(Is)(Ih)AR epidemic model which might be of potential interest in the characterization and control of the COVID-19 pandemic evolution. The proposed model incorporates both asymptomatic infectious and hospitalized infectious subpopulations to the standard infectious subpopulation of the classical SEIR model. In parallel, it also incorporates feedback vaccination and antiviral treatment controls. The exposed subpopulation has three different transitions to the three kinds of infectious subpopulations under eventually different proportionality parameters. The existence of a unique disease-free equilibrium point and a unique endemic one is proved together with the calculation of their explicit components. Their local asymptotic stability properties and the attainability of the endemic equilibrium point are investigated based on the next generation matrix properties, the value of the basic reproduction number, and nonnegativity properties of the solution and its equilibrium states. The reproduction numbers in the presence of one or both controls is linked to the control-free reproduction number to emphasize that such a number decreases with the control gains. We also prove that, depending on the value of the basic reproduction number, only one of them is a global asymptotic attractor and that the solution has no limit cycles.

scholarly journals Mathematical modeling and optimal intervention strategies of the COVID-19 outbreak

2021 ◽  
Author(s):  
Jayanta Mondal ◽  
Subhas Khajanchi
Keyword(s):  
Optimal Control ◽  
Basic Reproduction Number ◽  
Disease Transmission ◽  
Numerical Solutions ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Intervention Strategy ◽  
Intervention Strategies ◽  
Qualitative Behavior ◽  
The Basic Reproduction Number

Abstract 32,737,939 active cases and 438,210 deaths because of COVID-19 pandemic were recorded on 30 August 2021 in India. To end this ongoing global COVID-19 pandemic, there is an urgent need to implement multiple population-wide policies like social distancing, testing more people and contact tracing. To predict the course of the pandemic and come up with a strategy to control it effectively, a compartmental model has been established. The following six stages of infection are taken into consideration: susceptible ($S$), asymptomatic infected ($A$), clinically ill or symptomatic infected ($I$), quarantine ($Q$), isolation ($J$) and recovered ($R$), collectively termed as SAIQJR. The qualitative behavior of the model and the stability of biologically realistic equilibrium points are investigated in terms of the basic reproduction number. We performed sensitivity analysis with respect to the basic reproduction number and obtained that the disease transmission rate has an impact in mitigating the spread of diseases. Moreover, considering the non-pharmaceutical and pharmaceutical intervention strategies as control functions, an optimal control problem is implemented to mitigate the disease fatality. To reduce the infected individuals and to minimize the cost of the controls, an objective functional has been constructed and solved with the aid of Pontryagin's Maximum Principle. The implementation of optimal control strategy at the start of a pandemic tends to decrease the intensity of epidemic peaks, spreading the maximal impact of an epidemic over an extended time period. Extensive numerical simulations show that the implementation of intervention strategy has an impact in controlling the transmission dynamics of COVID-19 epidemic. Further, our numerical solutions exhibit that the combination of three controls are more influential when compared with the combination of two controls as well as single control. Therefore the implementation of all the three control strategies may help to mitigate novel coronavirus disease transmission at this present epidemic scenario.

scholarly journals Analyzing the MERS disease control strategy through an optimal control problem

2018 ◽  
Vol 28 (1) ◽  
pp. 169-184 ◽  
Author(s):  
Dipo Aldila ◽  
Herningtyas Padma ◽  
Khusnul Khotimah ◽  
Bevina Desjwiandra ◽  
Hengki Tasman
Keyword(s):  
Optimal Control ◽  
Supportive Care ◽  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Initial Conditions ◽  
Infected People ◽  
Intervention Costs ◽  
Supportive Care Intervention ◽  
The Basic Reproduction Number

AbstractA deterministic mathematical model of the Middle East respiratory syndrome (MERS) disease is introduced. Medical masks, supportive care treatment and a government campaign about the importance of medical masks will be involved in the model as time dependent variables. The problem is formulated as an optimal control one to minimize the number of infected people and keep the intervention costs as low as possible. Assuming that all control variables are constant, we find a disease free equilibrium point and an endemic equilibrium point explicitly. The existence and local stability criteria of these equilibria depend on the basic reproduction number. A sensitivity analysis of the basic reproduction number with respect to control parameters tells us that the intervention on medical mask use and the campaign about the importance of medical masks are much more effective for reducing the basic reproduction number than supportive care intervention. Numerical experiments for optimal control problems are presented for three different scenarios, i.e., a scenario of different initial conditions for the human population, a scenario of different initial basic reproduction numbers and a scenario of different budget limitations. Under budget limitations, it is much better to implement the medical mask intervention in the field, rather than give supportive care to control the spread of the MERS disease in the endemic prevention scenario. On the other hand, the medical mask intervention should be implemented partially together with supportive care to obtain the lowest number of infected people, with the lowest cost in the endemic reduction scenario.

scholarly journals The effect of control measures on COVID-19 transmission in Italy: Comparison with Guangdong province in China

2020 ◽  
Author(s):  
Peiyu Liu ◽  
Sha He ◽  
Libin Rong ◽  
Sanyi Tang
Keyword(s):  
Basic Reproduction Number ◽  
Media Coverage ◽  
Reproduction Number ◽  
Control Measures ◽  
Seir Model ◽  
Diagnosis Rate ◽  
And Control ◽  
Parameter Values ◽  
Test Result ◽  
The Basic Reproduction Number

Abstract Background COVID-19 is spreading in many countries around the world. Italy is the hardest hit in Europe and its number of new infections is still increasing. This study aims to evaluate the reason for the rapidly growing epidemic in Italy.Methods We compared Italy’s data of outbreak and control measures with the province of Guangdong in China. Then, a modified SEIR model was applied to estimate the basic reproduction number. Finally, we utilized a time-dependent dynamic model to study the future disease dynamics in Italy.Results The comparison of specific measures implemented in the two places and the time when the measures were initiated shows that the prevention and control actions in Italy were not sufficiently timely and effective. Using a modified SEIR model, we estimated parameter values based on available cumulative data and calculate the basic reproduction number to be 4.32 before the national lockdown in Italy. Numerical simulations revealed that under a scenario in which very strict interventions are taken when the minimum contact rate is 1 with the exponential decreasing rate is 0.5 and the fast diagnosis rate is 0.5 with the exponential increasing rate is 0.5 (i.e. the test result will be available in two days). In this scenario, Italy will reach the peak (i.e. 23900) after 43 days.Conclusion This study suggests that Italy is currently in a very serious epidemic status since control measures such as blockade of schools, isolation, medical supports and media coverage are not sufficiently timely and effective.

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