scholarly journals Dog Rabies in Dhaka, Bangladesh, and Implications for Control

Processes ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1513
Author(s):  
Masud M A ◽  
Md Hamidul Islam ◽  
Muhaiminul Islam Adnan ◽  
Chunyoung Oh
Keyword(s):  
Basic Reproduction Number ◽  
Carrying Capacity ◽  
Reproduction Number ◽  
Control Strategies ◽  
Logistic Growth ◽  
Capacity Control ◽  
Pulse Vaccination ◽  
Vaccination Strategies ◽  
Environmental Carrying Capacity ◽  
Huge Challenge

Controlling rabies among free-roaming street dogs has been a huge challenge in many parts of the world. Vaccination is a commonly used strategy to control rabies, however, sufficient vaccination coverage is very challenging when it comes to street dogs. Also, dog rabies data is scarce, making it difficult to develop proper strategies. In this study, we use a logistic growth incorporated epidemic model to understand the prevalence of rabies in the dog population of Dhaka, Bangladesh. The study shows that, the basic reproduction number for dog rabies in Dhaka lies between 1.1 to 1.249 and the environmental carrying capacity lies approximately between 58,110 to 194,739. Considering the vaccination and neuter programs administered in the last decade, we attempt to explain rabies transmission among dogs in this population. We found that the high basic reproduction number is associated with high environmental carrying capacity and vice versa. Further, we compare different type of control strategies, viz., constant vaccination, pulse vaccination, and optimal vaccination strategies. In the case of high environmental carrying capacity, vaccination, and neuter strategy is not sufficient for controlling rabies in street dogs, whereas carrying capacity control through waste management coupled with vaccination and neuter is more effective.

scholarly journals Threshold Dynamics of a Huanglongbing Model with Logistic Growth in Periodic Environments

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Jianping Wang ◽  
Shujing Gao ◽  
Yueli Luo ◽  
Dehui Xie
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Logistic Growth ◽  
Threshold Dynamics ◽  
Global Dynamics ◽  
Globally Asymptotically Stable ◽  
Linear Integral ◽  
The Impact ◽  
Disease Free ◽  
The Basic Reproduction Number

We analyze the impact of seasonal activity of psyllid on the dynamics of Huanglongbing (HLB) infection. A new model about HLB transmission with Logistic growth in psyllid insect vectors and periodic coefficients has been investigated. It is shown that the global dynamics are determined by the basic reproduction numberR0which is defined through the spectral radius of a linear integral operator. IfR0< 1, then the disease-free periodic solution is globally asymptotically stable and ifR0> 1, then the disease persists. Numerical values of parameters of the model are evaluated taken from the literatures. Furthermore, numerical simulations support our analytical conclusions and the sensitive analysis on the basic reproduction number to the changes of average and amplitude values of the recruitment function of citrus are shown. Finally, some useful comments on controlling the transmission of HLB are given.

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.

A MULTI-GROUP SVEIR EPIDEMIC MODEL WITH DISTRIBUTED DELAY AND VACCINATION

2012 ◽  
Vol 05 (03) ◽  
pp. 1260001 ◽  
Author(s):  
JINLIANG WANG ◽  
YASUHIRO TAKEUCHI ◽  
SHENGQIANG LIU
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Distributed Delay ◽  
Necessary Condition ◽  
Global Dynamics ◽  
Vaccination Strategies ◽  
Graph Theoretical Approach ◽  
Number Formula ◽  
Next Generation Matrix ◽  
The Basic Reproduction Number

In this paper, based on a class of multi-group epidemic models of SEIR type with bilinear incidences, we introduce a vaccination compartment, leading to multi-group SVEIR model. We establish that the global dynamics are completely determined by the basic reproduction number [Formula: see text] which is defined by the spectral radius of the next generation matrix. Our proofs of global stability of the equilibria utilize a graph-theoretical approach to the method of Lyapunov functionals. Mathematical results suggest that vaccination is helpful for disease control by decreasing the basic reproduction number. However, there is a necessary condition for successful elimination of disease. If the time for the vaccines to obtain immunity or the possibility for them to be infected before acquiring immunity is neglected in each group, this condition will be satisfied and the disease can always be eradicated by suitable vaccination strategies. This may lead to over evaluation for the effect of vaccination.

scholarly journals Global convergence of COVID-19 basic reproduction number and estimation from early-time SIR dynamics

2020 ◽  
Author(s):  
Gabriel G. Katul ◽  
Assaad Mrad ◽  
Sara Bonetti ◽  
Gabriele Manoli ◽  
Anthony J. Parolari
Keyword(s):  
Global Convergence ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Control Strategies ◽  
Early Period ◽  
Early Time ◽  
World Health ◽  
Potential Control ◽  
The Usa ◽  
Early Phases

AbstractThe SIR (‘susceptible-infectious-recovered’) formulation is used to uncover the generic spread mechanisms observed by COVID-19 dynamics globally, especially in the early phases of infectious spread. During this early period, potential controls were not effectively put in place or enforced in many countries. Hence, the early phases of COVID-19 spread in countries where controls were weak offer a unique perspective on the ensemble-behavior of COVID-19 basic reproduction number Ro. The work here shows that there is global convergence (i.e. across many nations) to an uncontrolled Ro = 4.5 that describes the early time spread of COVID-19. This value is in agreement with independent estimates from other sources reviewed here and adds to the growing consensus that the early estimate of Ro = 2.2 adopted by the World Health Organization is low. A reconciliation between power-law and exponential growth predictions is also featured within the confines of the SIR formulation. Implications for evaluating potential control strategies from this uncontrolled Ro are briefly discussed in the context of the maximum possible infected fraction of the population (needed for assessing health care capacity) and mortality (especially in the USA given diverging projections). Model results indicate that if intervention measures still result in Ro> 2.7 within 49 days after first infection, intervention is unlikely to be effective in general for COVID-19. Current optimistic projections place mortality figures in the USA in the range of 100,000 fatalities. For fatalities to be confined to 100,000 requires a reduction in Ro from 4.5 to 2.7 within 17 days of first infection assuming a mortality rate of 3.4%.

scholarly journals Local Dynamics of an SVIR Epidemic Model with Logistic Growth

CAUCHY ◽  
2020 ◽  
Vol 6 (3) ◽  
pp. 122-132
Author(s):  
Joko Harianto ◽  
Inda Puspita Sari
Keyword(s):  
Stability Analysis ◽  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Local Stability ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
Logistic Growth ◽  
Asymptotically Stable ◽  
Local Stability Analysis ◽  
The Basic Reproduction Number

Discussion of local stability analysis of SVIR models in this article is included in the scope of applied mathematics. The purpose of this discussion was to provide results of local stability analysis that had not been discussed in some articles related to the SVIR model. The SVIR models discussed in this article involve logistics growth in the vaccinated compartment. The results obtained, i.e. if the basic reproduction number less than one and m is positive, then there is one equilibrium point i.e. E0 is locally asymptotically stable. In the field of epidemiology, this means that the disease will disappear from the population. However, if the basic reproduction number more than one and b1 more than b, then there are two equilibrium points i.e. disease-free equilibrium point denoted by E0 and the endemic equilibrium point denoted by E1*. In this case the endemic equilibrium point E1* is locally asymptotically stable. In the field of epidemiology, this means that the disease will remain in the population. The numerical simulation supports these results.

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.

ANALYSIS OF AN AGE-STRUCTURED HIV-1 INFECTION MODEL WITH LOGISTIC TARGET CELL GROWTH

2020 ◽  
Vol 28 (04) ◽  
pp. 927-944
Author(s):  
HUIJUAN LIU ◽  
FEI XU ◽  
JIA-FANG ZHANG
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Logistic Growth ◽  
Infection Model ◽  
Target Cells ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Age Structured ◽  
Hiv 1 ◽  
The Basic Reproduction Number

In this work, we construct an age-structured HIV-1 infection model to investigate the interplay between [Formula: see text] cells and viruses. In our model, we assume that the variations in the death rate of productively infected [Formula: see text] cells and the production rate of virus in infected cells are all age-dependent, and the target cells follow logistic growth. We perform mathematical analysis and prove the persistence of the semi-flow of the system. We calculate the basic reproduction number and prove the local and global stability of the steady states. We show that if the basic reproduction number is less than one, the disease-free equilibrium is globally asymptotically stable, and if the basic reproduction number is greater than one, the infected steady state is locally asymptotically stable.

Dynamical Analysis of a Fractional-Order Hantavirus Infection Model

2020 ◽  
Vol 21 (2) ◽  
pp. 171-181 ◽  
Author(s):  
Mahmoud Moustafa ◽  
Mohd Hafiz Mohd ◽  
Ahmad Izani Ismail ◽  
Farah Aini Abdullah
Keyword(s):  
Fractional Order ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Fractional Order System ◽  
Order System ◽  
Logistic Growth ◽  
Hantavirus Infection ◽  
Infection Model ◽  
The Impact

AbstractThis paper considers a Hantavirus infection model consisting of a system of fractional-order ordinary differential equations with logistic growth. The fractional-order model describes the spread of Hantavirus infection in a system consisting of a population of susceptible and infected mice. The existence, uniqueness, non-negativity and boundedness of the solutions are established. In addition, the local and global asymptotic stability of the equilibrium points of the fractional order system and the basic reproduction number are studied. The impact of basic reproduction number and carrying capacity on the stability of the fractional order system are also theoretically and numerically investigated.

scholarly journals Qualitative analysis and optimal control of an SIR model with logistic growth, non-monotonic incidence and saturated treatment

2021 ◽  
Author(s):  
Jayanta Kumar Ghosh ◽  
Prahlad Majumdar ◽  
Uttam Ghosh
Keyword(s):  
Optimal Control ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Sir Model ◽  
Logistic Growth ◽  
Treatment Rate ◽  
Globally Asymptotically Stable ◽  
Susceptible Population ◽  
Saturated Treatment

This paper describes an SIR model with logistic growth rate of susceptible population, non-monotonic incidence rate and saturated treatment rate. The existence and stability analysis of equilibria have been investigated. It has been shown that the disease free equilibrium point ( DFE ) is globally asymptotically stable if the basic reproduction number is less than unity and the transmission rate of infection less than some threshold. The system exhibits the transcritical bifurcation at DFE with respect to the cure rate. We have also found the condition for occurring the backward bifurcation, which implies the value of basic reproduction number less than unity is not enough to eradicate the disease. Stability or instability of different endemic equilibria has been shown analytically. The system also experiences the saddle-node and Hopf bifurcation. The existence of Bogdanov - Takens bifurcation ( BT ) of co-dimension 2 has been investigated which has also been shown through numerical simulations. Here we have used two control functions, one is vaccination control and other is treatment control. We have solved the optimal control problem both analytically and numerically. Finally, the efficiency analysis has been used to determine the best control strategy among vaccination and treatment.

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.

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