Optimal Vaccination Problems for the Stochastic SIR Model with Saturated Treatment

Ishikawa, Masatoshi

doi:10.5687/sss.2013.203

Cited by 3 publications

(5 citation statements)

References 16 publications

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“…7. In this case, the stochastic DFS is given by (S f ,I f ,A f , V f ) ∼ = (0.47,0,0,0.53) from (12). Figure 7 shows that each population density converges to the the stochastic DFS.…”

Section: Dx(t) = F (X(t))dt + G(x(t))dw(t)mentioning

confidence: 96%

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On the Stability Analysis for the Stochastic Infectious Model under Subclinical Infections and Vaccination with Waning Immunity

Ishikawa

2023

Transactions of ISCIE

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This paper is concerned with the mathematical analysis of the stochastic infectious model under subclinical infections and vaccination and waning immunity. In the modern society with the advanced medical technology, we have still various kinds of the infectious disease threat including Coronavirus disease . Hence, the control and the analysis of infection diseases is one of major problems in epidemiology. In the control of the infectious diseases, vaccination plays an important role. In the realistic spread of the infectious disease, environmental change and individual difference cause some kinds of random fluctuations in the infection and the recovery rates. Moreover, noting that one of characteristics of Covid-19 is the existence of subclinical infections, we propose the stochastic infectious model under subclinical infections and vaccination with waning immunity. Since the stability analysis of the infectious model is effective in the control of the spread of the infectious disease, we analyze the stability of the stochastic infectious model. We derive the stability conditions for the proposed stochastic infectious model to be stable. By numerical simulations, we show the efficacy of the stability theorems derived in this paper and we study the influence of the random noise and vaccination on the stability.

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“…7. In this case, the stochastic DFS is given by (S f ,I f ,A f , V f ) ∼ = (0.47,0,0,0.53) from (12). Figure 7 shows that each population density converges to the the stochastic DFS.…”

Section: Dx(t) = F (X(t))dt + G(x(t))dw(t)mentioning

confidence: 96%

“…If the DFS is stable, even if the infectious disease breaks, prevalence of disease has eventually ended. On the other hand, if the ES is stable, we are not able to control the spread of the infectious disease without the effective vaccination policy [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

On the Stability Analysis for the Stochastic Infectious Model under Subclinical Infections and Vaccination with Waning Immunity

Ishikawa

2023

Transactions of ISCIE

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“…Remark 1: The integrand with respect to s in the 2nd term of the R.H.S. in (7) means the population size of dying before age a+s at time t+s. Hence, the 2nd term of the R.H.S.…”

Section: Deterministic Age-structured Infectious Modelmentioning

confidence: 99%

On the Mathematical Analysis of the Stochastic Age-structured Infectious Model

Ishikawa

2023

Stochastic Systems Theory and its Applications (SSS)

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The stability of the stochastic age-structured infectious model is studied in this paper. At present, we have still various kinds of the infectious disease threats including Corona virus disease, influenza and monkeypox. Hence, the analysis of infection diseases plays an important role in the modern society. In the past, a great deal of research of infectious diseases has been performed using various kinds of mathematical tools and models. Most of the conventional research is based on the deterministic mathematical tools and models. However, in the realistic spread of the infectious disease, environmental change and individual difference cause some kinds of random fluctuations in the infection, the recovery rates and the vaccination effect. Moreover, the parameters of the population dynamics such as infection, recovery, birth and death rates depend on age. Taking these facts into consideration, we propose the stochastic age-structured infectious model. Since the spread of infection has reference to the stability of the steady state of the stochastic infectious models, we consider the stability of the stochastic infectious models and derive the sufficient conditions for the steady state to be stable by using the stochastic Lyapunov theorem.

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“…An earlier version of this paper appeared in [13]. The present paper is a more complete version which contains the illustrative numerical example.…”

Section: Introductionmentioning

confidence: 99%

“…tion 5, we verify the efficiency of the proposed optimal vaccination strategy by numerical simulations. An earlier version of this paper appeared in [13]. The present paper is a more complete version which contains the illustrative numerical example.…”

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confidence: 99%

Optimal Vaccination Strategy under Saturated Treatment using the Stochastic SIR Model

Ishikawa

2013

Transactions of ISCIE

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This paper is concerned with the control strategy by vaccination of the infectious disease spread in the populations consisting of the susceptible, the infected and the recovered (SIR). In the realistic spread of the infectious disease, changes in the environment and the weather cause some kinds of random fluctuations in the infection and the recovery rates, etc. Moreover, medical facilities have generally the maximal capacity for treatment of diseases. Taking these facts into consideration, we propose the stochastic infectious model with vaccination and saturated treatment, and we consider the stochastic optimal vaccination problem for the SIR model with saturated treatment using the stochastic maximum principle and the four-step scheme. We construct a feasible optimal vaccination system. By numerical simulations, we validate the efficacy of the optimal vaccination strategy.

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Optimal Vaccination Problems for the Stochastic SIR Model with Saturated Treatment

Cited by 3 publications

References 16 publications

On the Stability Analysis for the Stochastic Infectious Model under Subclinical Infections and Vaccination with Waning Immunity

On the Stability Analysis for the Stochastic Infectious Model under Subclinical Infections and Vaccination with Waning Immunity

On the Mathematical Analysis of the Stochastic Age-structured Infectious Model

Optimal Vaccination Strategy under Saturated Treatment using the Stochastic SIR Model

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