On the almost sure convergence of a stochastic process in a class of nonlinear multi-population behavioral models for HIV/AIDS with delayed ART treatment

Wanduku, Divine

doi:10.1080/07362994.2020.1848593

Cited by 2 publications

(4 citation statements)

References 27 publications

(68 reference statements)

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“…where, P τ V S (t|r), P τ M AC V I |I(t) (t|r) and P τ V N D (t|r) are conditional survival probabilities for τ V S , τ M AC V I and τ V N D over (r, t] defined in (a1.-a7. ), respectively, and from (17),…”

Section: Derivation Of the Svis Modelmentioning

confidence: 99%

“…The existence of a disease-free equilibrium serves as a prelude for investigating disease eradication for the system (cf. [17]). Since asymptotically, (37)-( 38) becomes (43), whenever Assumption 3.2 holds, and the coefficients of the NANLS (32)-( 34) are HRFs with various shapes in Hypothesis 5.1(H1.-H4.…”

Section: Existence Of the Asymptotic Disease-free Equilibrium (Adfe)mentioning

confidence: 99%

“…disease eradication and disease persistence) in the system are investigated by examining the qualitative properties of the equilibria (cf. [16,17]). On the other hand, epidemic models with NANLS of o.d.e.s (cf.…”

Section: Introductionmentioning

confidence: 99%

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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: Derivation Of the Svis Modelmentioning

confidence: 99%

Section: Existence Of the Asymptotic Disease-free Equilibrium (Adfe)mentioning

confidence: 99%

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

Wanduku

2023

Preprint

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“…In this section, a more critical look at the BRN R 0 in (32) is taken to determine the effects of the supply of ODAs, delayed ART treatment, and withdrawal from treatment on the BRN R 0 , in order to find conditions for disease eradication. The reader is directed to the studies [33,34] for more results on the sensitivity of the BRN (32) to random fluctuations and noises in the HIV/AIDS disease dynamics. Remark 6.1.…”

Section: Stability Of the Dfe On The Finite Dimensional Phase Space Rmentioning

confidence: 99%

Finite- and multi-dimensional state representations and some fundamental asymptotic properties of a family of nonlinear multi-population models for HIV/AIDS with ART treatment and distributed delays

Wanduku¹

2022

DCDS-S

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A multipopulation HIV/AIDS deterministic epidemic model is studied. The population structure is a multihuman behavioral structure composed of humans practicing varieties of distinct HIV/AIDS preventive measures learnt from information and education campaigns (IEC) in the community. Antiretroviral therapy (ART) treatment is considered, and the delay from HIV exposure until the onset of ART is considered. The effects of national and multilateral support providing official developmental assistance (ODAs) to combat HIV are represented. A separate dynamics for the IEC information density in the community is derived. The epidemic model is a system of differential equations with random delays. The basic reproduction number (BRN) for the dynamics is obtained, and stability analysis of the system is conducted, whereby other disease control conditions are obtained in a multi-and a finite dimensional phase space. Numerical simulation results are given.

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On the almost sure convergence of a stochastic process in a class of nonlinear multi-population behavioral models for HIV/AIDS with delayed ART treatment

Cited by 2 publications

References 27 publications

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

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

Finite- and multi-dimensional state representations and some fundamental asymptotic properties of a family of nonlinear multi-population models for HIV/AIDS with ART treatment and distributed delays

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