A Mathematical Model and Analysis of an SVEIR Model for Streptococcus Pneumonia with Saturated Incidence Force of Infection

Zephaniah, Opara Chiekezi; Nwaugonma, Uche-Iwe Ruth; Chioma, Inyama Simeon; Adrew, Omame

doi:10.11648/j.mma.20200501.13

Cited by 10 publications

(3 citation statements)

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“…Model matematika untuk penyakit menular telah diakui sebagai metode yang dapat memberikan pemahaman mengenai dinamika infeksi dalam tubuh, dinamika penularan dalam populasi manusia, dan perumusan atau implementasi program pengendalian penyakit [9]. Penelitian model matematika penyebaran penyakit pneumonia telah banyak dilakukan, antara lain; model matematika penyebaran penyakit pneumonia dengan faktor vaksin [11] dan model matematika penyebaran penyakit pneumonia dengan model SV EIR [15].…”

Section: Pendahuluanunclassified

Model Matematika Penyebaran Penyakit Pneumonia dengan Intervensi Vaksinasi dan Pengobatan

Darmawan

Tasman

2022

jmi

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Pneumonia merupakan penyakit infeksi saluran pernapasan yang menyerang paruparu. Salah satu upaya yang dapat dilakukan untuk mengendalikan penyebaran penyakit ini adalah dengan melakukan pengobatan dan vaksinasi. Pada artikel ini dikonstruksi model matematika penyebaran penyakit pneumonia dengan intervensi pengobatan dan vaksinasi. Model matematika tersebut dikaji secara analitik dan dilakukan simulasi numerik. Kajian analitik meliputi keberadaan titik keseimbangan dan kestabilan lokalnya, serta bilangan reproduksi dasar R 0 . Dengan simulasi numerik didapat informasi bahwa intervensi vaksinasi dan pengobatan mampu mengendalikan penyebaran penyakit pneumonia.Kata kunci: epidemiologi matematika, titik keseimbangan, R 0 , kestabilan lokal.

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Section: Pendahuluanunclassified

Model Matematika Penyebaran Penyakit Pneumonia dengan Intervensi Vaksinasi dan Pengobatan

Darmawan

Tasman

2022

jmi

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“…Also, effective contacts between infected and uninfected humans may saturate at high infection peaks as a result of the crowding effect of infected individuals or as a result of control measures by the uninfected individuals [41]. The saturated incidence function best explains this, and has been adopted successfully in many epidemic models [42][43][44]. In biological models which deal with high co-endemicity of two diseases, this serves as the best incidence rate.…”

Section: Introductionmentioning

confidence: 99%

A Stochastic Model to Assess the Epidemiological Impact of Vaccine Booster Doses on COVID-19 and Viral Hepatitis B Co-Dynamics with Real Data

Omame,

Abbas,

Baleanu

2024

CMES

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A patient co-infected with COVID-19 and viral hepatitis B can be at more risk of severe complications than the one infected with a single infection. This study develops a comprehensive stochastic model to assess the epidemiological impact of vaccine booster doses on the co-dynamics of viral hepatitis B and COVID-19. The model is fitted to real COVID-19 data from Pakistan. The proposed model incorporates logistic growth and saturated incidence functions. Rigorous analyses using the tools of stochastic calculus, are performed to study appropriate conditions for the existence of unique global solutions, stationary distribution in the sense of ergodicity and disease extinction. The stochastic threshold estimated from the data fitting is given by: R S 0 = 3.0651. Numerical assessments are implemented to illustrate the impact of double-dose vaccination and saturated incidence functions on the dynamics of both diseases. The effects of stochastic white noise intensities are also highlighted.

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“…Many epidemic models have since used the aforementioned incidence types. We will combine the incidence rates: Mathematical models of the classical integer-order derivative have been adopted in studying the dynamics of infectious diseases [20][21][22][23][24][25][26]. These models, due to the integer nature of the derivative constitute limitations.…”

Section: Introductionmentioning

confidence: 99%

Analysis of a non-integer order compartmental model for cholera and COVID-19 incorporating human and environmental transmissions

Usman,

Abbas,

Omame

2023

Phys. Scr.

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Fractional differential operators have increasingly gained wider applications in epidemiological modelling due to their ability to capture memory effect in their definitions; an attribute which lacks in the concept of classical integer derivatives. In this paper, employing the Caputo fractional operator with singular kernel, the co-dynamical model for cholera and COVID-19 diseases is proposed and analyzed, incorporating both direct and indirect transmission routes for cholera. The necessary conditions for existence of the unique solution of the proposed model are studied. Using the results from fixed point theory, Ulam-Hyers stability analysis of the system is performed. The model is fitted to real data from Pakistan and the optimized order of the fractional derivative for which the system fits well to data is obtained. Other numerical assessments of the model are also executed. Phase portraits of the infected classes with different initial conditions and various order of the fractional derivative are obtained in the cases when the reproduction number  0 < 1 and  0 > 1 . It is observed that the trajectories for the infected compartments tend towards the infection-free steady state when  0 < 1 and the endemic steady state when  0 > 1 irrespective of the initial conditions and the order of the fractional derivative. Increment in the COVID-19 vaccine efficacy, keeping the vaccination rate fixed at δ 1 ω = 0.8 , resulted in a decline in the COVID-19 disease. Also, increasing the COVID-19 vaccination rate, keeping the vaccine efficacy for COVID-19 fixed at ϕ c ω = 0.85 , led to a decline in the COVID-19 associated reproduction number. The simulations also pointed out the impact of COVID-19 and cholera vaccinations, direct and indirect transmissions of cholera.

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A Mathematical Model and Analysis of an SVEIR Model for Streptococcus Pneumonia with Saturated Incidence Force of Infection

Cited by 10 publications

References 0 publications

Model Matematika Penyebaran Penyakit Pneumonia dengan Intervensi Vaksinasi dan Pengobatan

Model Matematika Penyebaran Penyakit Pneumonia dengan Intervensi Vaksinasi dan Pengobatan

A Stochastic Model to Assess the Epidemiological Impact of Vaccine Booster Doses on COVID-19 and Viral Hepatitis B Co-Dynamics with Real Data

Analysis of a non-integer order compartmental model for cholera and COVID-19 incorporating human and environmental transmissions

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