Dynamics of swine influenza model with optimal control

A deterministic model for evaluating the impact of voluntary testing and treatment on the transmission dynamics of tuberculosis is formulated and analyzed. The epidemiological threshold, known as the reproduction number is derived and qualitatively used to investigate the existence and stability of the associated equilibrium of the model system. The disease-free equilibrium is shown to be locally-asymptotically stable when the reproductive number is less than unity, and unstable if this threshold parameter exceeds unity. It is shown, using the Centre Manifold theory, that the model undergoes the phenomenon of backward bifurcation where the stable disease-free equilibrium co-exists with a stable endemic equilibrium when the associated reproduction number is less than unity. The analysis of the reproduction number suggests that voluntary tuberculosis testing and treatment may lead to effective control of tuberculosis. Furthermore, numerical simulations support the fact that an increase voluntary tuberculosis testing and treatment have a positive impact in controlling the spread of tuberculosis in the community.

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Modeling the impact of early interventions on the transmission dynamics of coronavirus infection

F1000Research ◽

10.12688/f1000research.54268.1 ◽

2021 ◽

Vol 10 ◽

pp. 518

Author(s):

Christopher Saaha Bornaa ◽

Baba Seidu ◽

Yakubu Ibrahim Seini

Keyword(s):

Death Rate ◽

Deterministic Model ◽

Reproduction Number ◽

Equilibrium Points ◽

Transmission Probability ◽

Transmission Dynamics ◽

Early Interventions ◽

Coronavirus Infection ◽

The Impact ◽

Disease Free

A deterministic model is proposed to describe the transmission dynamics of coronavirus infection with early interventions. Epidemiological studies have employed modeling to unravel knowledge that transformed the lives of families, communities, nations and the entire globe. The study established the stability of both disease free and endemic equilibria. Stability occurs when the reproduction number, R0, is less than unity for both disease free and endemic equilibrium points. The global stability of the disease-free equilibrium point of the model is established whenever the basic reproduction number R0 is less than or equal to unity. The reproduction number is also shown to be directly related to the transmission probability (β), rate at which latently infected individuals join the infected class (δ) and rate of recruitment (Λ). It is inversely related to natural death rate (μ), rate of early treatment (τ1), rate of hospitalization of infected individuals (θ) and Covid-induced death rate (σ). The analytical results established are confirmed by numerical simulation of the model.

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TRANSMISSION DYNAMICS AND CONTROL STRATEGIES OF COVID-19 IN WUHAN, CHINA

Journal of Biological System ◽

10.1142/s0218339020500096 ◽

2020 ◽

Vol 28 (03) ◽

pp. 543-560 ◽

Cited By ~ 8

Author(s):

LIUYONG PANG ◽

SANHONG LIU ◽

XINAN ZHANG ◽

TIANHAI TIAN ◽

ZHONG ZHAO

Keyword(s):

Reproduction Number ◽

Control Strategies ◽

Public Awareness ◽

Control Measures ◽

Transmission Dynamics ◽

Published Data ◽

Model Parameters ◽

Strict Control ◽

Dynamics And Control ◽

Numerical Calculation Method

In December 2019, a novel coronavirus, SARS-COV-2, was identified among patients in Wuhan, China. Two strict control measures, i.e., putting Wuhan on lockdown and taking strict quarantine rule, were carried out to contain the spread of COVID-19. Based on the different control measures, we divided the transmission process of COVID-19 into three stages. An SEIHR model was established to describe the transmission dynamics and was applied to fit the published data on the confirmed cases of Wuhan city from December 31, 2019 to March 25, 2020 to deduce the time when the first patient with COVID-19 appeared. The basic reproduction number was estimated in the first stage to demonstrate the number of secondary infectious cases generated by an average infectious case in the absence of policy intervention. The effective reproduction numbers in second and third stages were estimated to evaluate the effects of the two strict control measures. In addition, sensitivity analysis of the reproduction number according to model parameters was executed to demonstrate the effect of the control measures for containing the spread of COVID-19. Finally, the numerical calculation method was applied to investigate the influence of the different control measures on the spread of COVID-19. The results indicated that following the strict quarantine rule was very effective, and reducing the effective contact rates and improving the diagnosis rate were crucial in reducing the effective reproduction number, and taking control measures as soon as possible can effectively contain a larger outbreak of COVID-19. But a bigger challenge for us to contain the spread of COVID-19 was the transmission from the asymptomatic carriers, which required to raising the public awareness of self-protection and keeping a good physical protection.

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Analysis of a mathematical model for the transmission dynamics of human melioidosis

International Journal of Biomathematics ◽

10.1142/s179352452050062x ◽

2020 ◽

Vol 13 (07) ◽

pp. 2050062

Author(s):

Yibeltal Adane Terefe ◽

Semu Mitiku Kassa

Keyword(s):

Human Population ◽

Deterministic Model ◽

Reproduction Number ◽

Backward Bifurcation ◽

Endemic Equilibrium ◽

Transmission Dynamics ◽

Asymptotically Stable ◽

Disease Dynamics ◽

Number Formula ◽

Disease Free

A deterministic model for the transmission dynamics of melioidosis disease in human population is designed and analyzed. The model is shown to exhibit the phenomenon of backward bifurcation, where a stable disease-free equilibrium co-exists with a stable endemic equilibrium when the basic reproduction number [Formula: see text] is less than one. It is further shown that the backward bifurcation dynamics is caused by the reinfection of individuals who recovered from the disease and relapse. The existence of backward bifurcation implies that bringing down [Formula: see text] to less than unity is not enough for disease eradication. In the absence of backward bifurcation, the global asymptotic stability of the disease-free equilibrium is shown whenever [Formula: see text]. For [Formula: see text], the existence of at least one locally asymptotically stable endemic equilibrium is shown. Sensitivity analysis of the model, using the parameters relevant to the transmission dynamics of the melioidosis disease, is discussed. Numerical experiments are presented to support the theoretical analysis of the model. In the numerical experimentations, it has been observed that screening and treating individuals in the exposed class has a significant impact on the disease dynamics.

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Mathematical Analysis of a Malaria Model with Partial Immunity to Reinfection

Abstract and Applied Analysis ◽

10.1155/2013/405258 ◽

2013 ◽

Vol 2013 ◽

pp. 1-17 ◽

Cited By ~ 5

Author(s):

Li-Ming Cai ◽

Abid Ali Lashari ◽

Il Hyo Jung ◽

Kazeem Oare Okosun ◽

Young Il Seo

Keyword(s):

Deterministic Model ◽

Reproduction Number ◽

Global Analysis ◽

Backward Bifurcation ◽

Mass Action ◽

Transmission Dynamics ◽

Global Dynamics ◽

Reinfection Rate ◽

Malaria Model ◽

Disease Free

A deterministic model with variable human population for the transmission dynamics of malaria disease, which allows transmission by the recovered humans, is first developed and rigorously analyzed. The model reveals the presence of the phenomenon of backward bifurcation, where a stable disease-free equilibrium coexists with one or more stable endemic equilibria when the associated reproduction number is less than unity. This phenomenon may arise due to the reinfection of host individuals who recovered from the disease. The model in an asymptotical constant population is also investigated. This results in a model with mass action incidence. A complete global analysis of the model with mass action incidence is given, which reveals that the global dynamics of malaria disease with reinfection is completely determined by the associated reproduction number. Moreover, it is shown that the phenomenon of backward bifurcation can be removed by replacing the standard incidence function with a mass action incidence. Graphical representations are provided to study the effect of reinfection rate and to qualitatively support the analytical results on the transmission dynamics of malaria.

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Modeling the impact of early interventions on the transmission dynamics of coronavirus infection

F1000Research ◽

10.12688/f1000research.54268.2 ◽

2021 ◽

Vol 10 ◽

pp. 518

Author(s):

Christopher Saaha Bornaa ◽

Baba Seidu ◽

Yakubu Ibrahim Seini

Keyword(s):

Death Rate ◽

Deterministic Model ◽

Reproduction Number ◽

Equilibrium Points ◽

Transmission Probability ◽

Transmission Dynamics ◽

Early Interventions ◽

Coronavirus Infection ◽

The Impact ◽

Disease Free

A deterministic model is proposed to describe the transmission dynamics of coronavirus infection with early interventions. Epidemiological studies have employed modeling to unravel knowledge that transformed the lives of families, communities, nations and the entire globe. The study established the stability of both disease free and endemic equilibria. Stability occurs when the reproduction number, R0, is less than unity for both disease free and endemic equilibrium points. The global stability of the disease-free equilibrium point of the model is established whenever the basic reproduction number R0 is less than or equal to unity. The reproduction number is also shown to be directly related to the transmission probability (β), rate at which latently infected individuals join the infected class (δ) and rate of recruitment (Λ). It is inversely related to natural death rate (μ), rate of early treatment (τ1), rate of hospitalization of infected individuals (θ) and Covid-induced death rate (σ). The analytical results established are confirmed by numerical simulation of the model.

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Mathematical Model of Three Age-Structured Transmission Dynamics of Chikungunya Virus

Computational and Mathematical Methods in Medicine ◽

10.1155/2016/4320514 ◽

2016 ◽

Vol 2016 ◽

pp. 1-31 ◽

Cited By ~ 11

Author(s):

Folashade B. Agusto ◽

Shamise Easley ◽

Kenneth Freeman ◽

Madison Thomas

Keyword(s):

Age Structure ◽

Stable Disease ◽

Chikungunya Virus ◽

Deterministic Model ◽

Reproduction Number ◽

Age Distribution ◽

Transmission Dynamics ◽

Globally Asymptotically Stable ◽

Age Structured ◽

Disease Free

We developed a new age-structured deterministic model for the transmission dynamics of chikungunya virus. The model is analyzed to gain insights into the qualitative features of its associated equilibria. Some of the theoretical and epidemiological findings indicate that the stable disease-free equilibrium is globally asymptotically stable when the associated reproduction number is less than unity. Furthermore, the model undergoes, in the presence of disease induced mortality, the phenomenon of backward bifurcation, where the stable disease-free equilibrium of the model coexists with a stable endemic equilibrium when the associated reproduction number is less than unity. Further analysis of the model indicates that the qualitative dynamics of the model are not altered by the inclusion of age structure. This is further emphasized by the sensitivity analysis results, which shows that the dominant parameters of the model are not altered by the inclusion of age structure. However, the numerical simulations show the flaw of the exclusion of age in the transmission dynamics of chikungunya with regard to control implementations. The exclusion of age structure fails to show the age distribution needed for an effective age based control strategy, leading to a one size fits all blanket control for the entire population.

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Assessing the effects of time-dependent restrictions and control actions to flatten the curve of COVID-19 in Kazakhstan

PeerJ ◽

10.7717/peerj.10806 ◽

2021 ◽

Vol 9 ◽

pp. e10806

Author(s):

Ton Duc Do ◽

Meei Mei Gui ◽

Kok Yew Ng

Keyword(s):

Ad Hoc ◽

Reproduction Number ◽

National Level ◽

Control Measures ◽

Time Dependent ◽

Transmission Dynamics ◽

Model Parameters ◽

Real World Data ◽

Control Actions ◽

And Control

This article presents the assessment of time-dependent national-level restrictions and control actions and their effects in fighting the COVID-19 pandemic. By analysing the transmission dynamics during the first wave of COVID-19 in the country, the effectiveness of the various levels of control actions taken to flatten the curve can be better quantified and understood. This in turn can help the relevant authorities to better plan for and control the subsequent waves of the pandemic. To achieve this, a deterministic population model for the pandemic is firstly developed to take into consideration the time-dependent characteristics of the model parameters, especially on the ever-evolving value of the reproduction number, which is one of the critical measures used to describe the transmission dynamics of this pandemic. The reproduction number alongside other key parameters of the model can then be estimated by fitting the model to real-world data using numerical optimisation techniques or by inducing ad-hoc control actions as recorded in the news platforms. In this article, the model is verified using a case study based on the data from the first wave of COVID-19 in the Republic of Kazakhstan. The model is fitted to provide estimates for two settings in simulations; time-invariant and time-varying (with bounded constraints) parameters. Finally, some forecasts are made using four scenarios with time-dependent control measures so as to determine which would reflect on the actual situations better.

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A Mathematical Model of Treatment and Vaccination Interventions of Pneumococcal Pneumonia Infection Dynamics

Journal of Applied Mathematics ◽

10.1155/2018/2539465 ◽

2018 ◽

Vol 2018 ◽

pp. 1-16 ◽

Cited By ~ 4

Author(s):

Mohammed Kizito ◽

Julius Tumwiine

Keyword(s):

Reproduction Number ◽

Control Strategies ◽

The Elderly ◽

Infection Dynamics ◽

And Control ◽

Long Term Behavior ◽

The Impact ◽

Globally Stable ◽

Disease Free

Streptococcus pneumoniae is one of the leading causes of serious morbidity and mortality worldwide, especially in young children and the elderly. In this study, a model of the spread and control of bacterial pneumonia under public health interventions that involve treatment and vaccination is formulated. It is found out that the model exhibits the disease-free and endemic equilibria. The disease-free equilibrium is stable if and only if the basic reproduction number R0<1 and the disease will be wiped out of the population. For R0≥1, the endemic equilibrium is globally stable and the disease persists. We infer the effect of these interventions on the dynamics of the pneumonia through sensitivity analysis on the effective reproduction number Re, from which it is revealed that treatment and vaccination interventions combined can eradicate pneumonia infection. Numerical simulation to illustrate the analytical results and establish the long term behavior of the disease is done. The impact of pneumonia infection control strategies is investigated. It is revealed that, with treatment and vaccination interventions combined, pneumonia can be wiped out. However, with treatment intervention alone, pneumonia persists in the population.

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Parameter Estimation of COVID-19 Pandemic Model with Self Protection Behavior Changes

10.1101/2020.08.24.20180695 ◽

2020 ◽

Author(s):

Kassahun Getnet Mekonen ◽

Tatek Getachew Habtemicheal ◽

Shiferaw Feyissa Balcha

Keyword(s):

Equilibrium Point ◽

Reproduction Number ◽

Transmission Dynamics ◽

Estimation Methods ◽

Behavior Changes ◽

Model Parameters ◽

Sensitivity Index ◽

Self Protection ◽

Sensitive Parameters ◽

Disease Free

A mathematical model for the transmission dynamics of Coronavirus diseases (COVID-19) is proposed by incorporating self-protection behavior changes in the population. The disease-free equilibrium point is computed and its stability analysis is studied. The basic reproduction number(R 0 ) of the model is computed and the disease-free equilibrium point is locally and globally stable for R 0<1 and unstable for R 0 >1. Based on the available data the unknown model parameters are estimated using a combination of least square and Bayesian estimation methods for different countries. Using forward sensitivity index the model parameters are carried out to determine and identify the key factors for the spread of disease dynamics. From country to country the sensitive parameters for the spread of the virus varies. It is found out that the reproduction number depends mostly on the infection rates, the threshold value of the force of infection for a population, the recovery rates, and the virus decay rate in the environment. It is also demonstrated that control of the effective transmission rate (recommended human behavioral change towards self-protective measures) is essential to stop the spreading of the virus. Numerical simulations also show that the virus transmission dynamics depend mostly on those sensitive parameters.

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