Pulse vaccination in SIRS epidemic model with non-monotonic incidence rate

Gakkhar, Sunita; Negi, K. S.

doi:10.1016/j.chaos.2006.05.054

Cited by 58 publications

(31 citation statements)

References 8 publications

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“…The simplest forms of these models are ordinary differential equations (O.D.E) [14,15]. In recent years, epidemic models described by ordinary differential equation have been studied and extended by many authors ( see, for examples [5,12,18,25,26,30,31,32] and references cited therein). In [23] a system of ODEs with a general incidence term f(S,I) is studied, conditions are found on f under which the standard threshold behaviour occurs;the disease free equilibrium is globally asymptotically stable for R 0 < 1 and endemic equilibrium is globally asymptotically stable for R 0 > 1.…”

Section: Introductionmentioning

confidence: 99%

Optimal Control Analysis of an SIR Epidemic Model with Constant recruitment

Bakare

Nwagwo²,

Danso-Addo³

2014

International Journal of Applied Mathematical Research

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A mathematical model of an SIR epidemic model with constant recruitment and two control variables using control terms and a deterministic system of differential equation is presented and analyzed mathematically and numerically. We intend to control the susceptible and infected individuals with educational campaign and treatment strategies. We analyzed the model by non-dimensionalizing the system of equations of our SIR epidemic model and derived our basic reproduction number.We aim to minimize the total number of infective individuals and the cost associated with the use of educational campaign and treatment on [0, T ]. We used Pontryagin's maximum principle to characterize the optimal levels of the two controls. The resulting optimality system is solved numerically. The results show that the optimal combination of treatment and educational campaign strategy required to achieve the set objective will depend on the relative cost of each of the control measures. The results from our simulation is discussed.

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Section: Introductionmentioning

confidence: 99%

Optimal Control Analysis of an SIR Epidemic Model with Constant recruitment

Bakare

Nwagwo²,

Danso-Addo³

2014

International Journal of Applied Mathematical Research

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“…The pulse vaccination strategy (PVS) consists of repeated application of vaccine at discrete time with equal interval in a population in contrast to the traditional constant vaccination (Gakkhar and Negi 2008;Zhou and Liu 2003). Compared to the proportional vaccination models, the study of pulse vaccination models is in its infancy (Zhou and Liu 2003).…”

Section: Introductionmentioning

confidence: 99%

“…At each vaccination time a constant fraction of the susceptible population is vaccinated successfully. Since 1993, attempts have been made to develop mathematical theory to control infectious diseases using pulse vaccination (Agur et al 1993;Gakkhar and Negi 2008). Nokes and Swinton (1995) discussed the control of childhood viral infections by pulse vaccination strategy.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Analysis of a Chlamydia Epidemic Model with Pulse Vaccination Strategy

Samanta

2014

Acta Biotheor

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In this paper, we have considered a dynamical model of Chlamydia disease with varying total population size, bilinear incidence rate and pulse vaccination strategy. We have defined two positive numbers R₀ and (R₁≤ R₀). It is proved that there exists an infection-free periodic solution which is globally attractive if R₀ < 1 and the disease is permanent if R₁> 1 The important mathematical findings for the dynamical behaviour of the Chlamydia disease model are also numerically verified using MATLAB. Finally epidemiological implications of our analytical findings are addressed critically.

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“…Today, we usually call these compartmental models SIR models or SIRS models with each letter referring to a 'compartment' in which an individual can reside. The SIR models and SIRS models have been studied in many literatures [2,[4][5][6]13,14,[17][18][19]25,26,38,40]. In particular, Jaime Mena-Lorca and Herbert W. Hethcote [26] considered five SIRS epidemiological models for populations of varying size.…”

Section: Introductionmentioning

confidence: 99%

An impulsive delayed SEIRS epidemic model with saturation incidence

Zhang

Teng

2008

Journal of Biological Dynamics

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A delayed SEIRS epidemic model with pulse vaccination and saturation incidence rate is investigated. Using Krasnoselskii's fixed-point theorem, we obtain the existence of infection-free periodic solution of the impulsive delayed epidemic system. We define some new threshold values R 1 , R 2 and R 3 . Further, using the comparison theorem, we obtain the explicit formulae of R 1 and R 2 . Under the condition R 1 < 1, the infection-free periodic solution is globally attractive, and that R 2 > 1 implies that the disease is permanent. Theoretical results show that the disease will be extinct if the vaccination rate is larger than θ * and the disease is uniformly persistent if the vaccination rate is less than θ * . Our results indicate that a long latent period of the disease or a large pulse vaccination rate will lead to eradication of the disease. Moreover, we prove that the disease will be permanent as R 3 > 1.

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Pulse vaccination in SIRS epidemic model with non-monotonic incidence rate

Cited by 58 publications

References 8 publications

Optimal Control Analysis of an SIR Epidemic Model with Constant recruitment

Optimal Control Analysis of an SIR Epidemic Model with Constant recruitment

Mathematical Analysis of a Chlamydia Epidemic Model with Pulse Vaccination Strategy

An impulsive delayed SEIRS epidemic model with saturation incidence

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