Modelling the effect of booster vaccination on the transmission dynamics of diseases that spread by droplet infection

Misra, O. P.; Mishra, Dinesh Kumar

doi:10.1016/j.nahs.2009.06.001

Cited by 17 publications

(14 citation statements)

References 14 publications

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“…Vaccines are effective in reduction of the number of new cases and severity of the disease [21][22][23]. Childhood pneumonia is preventable through immunization with the effective two vaccines: Hib conjugate vaccine (HibCV) against the Haemophilus influenzae type b (Hib) and pneumococcal conjugate vaccine (PCV) against pneumococcus [24].…”

Section: Journal Of Applied Mathematicsmentioning

confidence: 99%

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

Kizito

2018

Journal of Applied Mathematics

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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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Section: Journal Of Applied Mathematicsmentioning

confidence: 99%

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

Kizito

2018

Journal of Applied Mathematics

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“…Using the comparison theorem of functional differential equations and Lemma 3.1, we have lim t!1 22) we conclude that the spread of the disease should be controlled by way of suitable protective measures of the society to reduce the values of b 1 (t) (transmission rate function from pathogens to susceptible humans through droplets) and b 2 (t) (transmission rate function from pathogens (bacteria and viruses) to susceptible humans through direct contact with infected person) and thereby to decrease R ⁄ . Every individual should follow simple steps as cough etiquettes (covering mouth and nose with handkerchief or tissue paper while coughing), stay at least an arm's length from persons coughing or sneezing, avoid gathering and washing hands frequently.…”

Section: ð3:18þmentioning

confidence: 99%

“…Alexander et al [1] analyzed the effect of a booster vaccination programme on disease epidemiology. Recently, Misra and Mishra [22] have proposed a mathematical model for studying the effects of booster dose vaccination on the dynamics of infectious diseases transmitted by droplet infection. All of these systems are modelled by autonomous differential equations.…”

Section: Introductionmentioning

confidence: 99%

Analysis of a nonautonomous dynamical model of diseases through droplet infection and direct contact

Samanta

2011

Applied Mathematics and Computation

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“…Kribs-Zaleta and Martcheva (2002), Kribs-Zaleta and Velasco-Harnandez (2000), Moghadas (2004), Moghadas and Gumel (2003) and Hethcote (2000) analysed the effect of single dose vaccine programme applied to infectious individuals using mathematical modellings. Alexander, Moghadas, Rohani, and Summers (2006), Anderson and Grenfell (1986), Dietz (1981), Misra and Mishra (2009) and Paulo, Gomes, Casinhas, and Horta (2000) studied the impact of multiple dose vaccination programme on the dynamics of infectious diseases. Recently, Samanta (2011) has proposed and analysed a nonautonomous dynamical model of diseases that spread by droplet infection and also through direct contact with varying total population size and distributed time delay to become infectious.…”

Section: Introductionmentioning

confidence: 99%

A delayed epidemic model of diseases through droplet infection and direct contact with saturation incidence and pulse vaccination

Samanta

Sen

Maiti³

2016

Systems Science & Control Engineering

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In this paper, we have considered a dynamical model of diseases that spread by droplet infection and also through direct contact with varying total population size and discrete time delay to become infectious. It is assumed that there is a latent period of the disease and an immune period of the recovered individuals. Pulse vaccination is an effective and important strategy for the elimination of infectious diseases and so we have analysed this model with pulse vaccination and saturation incidence rate. It is also assumed that the time lag due to lose of immunity of recovered individuals is equal to the interval between two pulses. We have defined two positive numbers R 1 and R 2. It is proved that there exists an infection-free periodic solution which is globally attractive if R 1 < 1 and the disease is permanent if R 2 > 1. The important mathematical findings for the dynamical behaviour of the model are also numerically verified using MATLAB. Finally epidemiological implications of our analytical findings are addressed critically.

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Modelling the effect of booster vaccination on the transmission dynamics of diseases that spread by droplet infection

Cited by 17 publications

References 14 publications

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

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

Analysis of a nonautonomous dynamical model of diseases through droplet infection and direct contact

A delayed epidemic model of diseases through droplet infection and direct contact with saturation incidence and pulse vaccination

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