On a Novel SVEIRS Markov chain epidemic model with multiple discrete delays and infection rates: modeling and sensitivity analysis to determine vaccination effects

Wanduku, Divine; Jegede, Omotomilola Onaopemipo; Rahul, Chinmoy Roy; Oluyede, Broderick O.; Farotimi, Oluwaseun

doi:10.1016/b978-0-32-399557-3.00009-0

Cited by 2 publications

(1 citation statement)

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“…Indeed, the essential mathematical principles for deriving the mass-action exponential rates β IS I(t) N ∆t and β IV I(t) N ∆t over the small time interval [t, t + ∆t) are the homogeneous mixing and mixture distributions, in particular, the Binomial-Poisson hierarchical mixture distribution model explained in [Theorem 3.1 [8,9]]; also see [10] . In this paper, the single transition events between the species S, V , and I denoted by S(t) → I(t) & V (t) → I(t), where the arrows "→" point to the direction of transition from one state to another, occur by mass-action contact (MAC).…”

Section: Introductionmentioning

confidence: 99%

Compartmental models with underlying renewal process: survival analysis and applications to SVIS epidemic models

Wanduku

2023

Preprint

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Compartmental models assuming exponentially distributed lifetime stages are limited because of a constant hazard rate. Here, a theoretical compartmental model for a system with general lifetime distributions is studied. The model represents the transition rates between jumps of a renewal process in the system. Applications are given for the SVIS disease epidemic model, to investigate the impacts of the hazard rate functions (HRFs) on disease control. The new SVIS model is a non-autonomous nonlinear system (NANLS) of ordinary differential equations (ODEs), with coefficients that are HRFs. Moreover, for a class of lifetime distributions, the NANLS of ODEs is asymptotically autonomous. Four asymptotic behaviors of the HRFs: a monotonic, a bathtub, a reverse bathtub and a constant shape are explored to determine the asymptotic population for disease eradication. Also, analysis is conducted to determine the sensitivity of the epidemic system to the hazard rate behaviors over time. Numerical simulation results are given for different lifetime models representing hazard behaviors for vaccine efficacy and immunity. 2000 MSC: 92B15, 62N05, 60E05, 92D25

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Section: Introductionmentioning

confidence: 99%