On the Effect of Vaccination, Screening and Treatment in Controlling Typhoid Fever Spread Dynamics: Deterministic and Stochastic Applications

Ogunlade, Temitope Olu; Ogunmiloro, Oluwatayo Michael; Ogunyebi, Segun Nathaniel; Fatoyinbo, Grace Ebunoluwa; Okoro, J. O.; Akindutire, Opeyemi Roselyn; Halid, O. Y.; Olubiyi, Adenike Oluwafunmilola

doi:10.13189/ms.2020.080601

Cited by 5 publications

(4 citation statements)

References 8 publications

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“…The norms are bounded because they exist. As a result, the drift and the diffusion matrices are bounded and, hence, satisfy the conditions for uniqueness and existence of the solution criteria [26].…”

Section: Existence and Uniqueness For The Stochastic Differentialmentioning

confidence: 93%

“…where XðtÞ = ðX 1 ðtÞ, X 2 ðtÞÞ T , WðtÞ = ðW 1 ðtÞ, W 2 ðtÞÞ T , f i ðX ðtÞ, tÞ is a 2-dimensional vector with entries f i ðx, tÞ and g ij ðXðtÞ, tÞ is a 2 × 2 matrix with entries g ij ðx, tÞ satisfy the following Lipschitz and growth conditions in the equations below for some constant k < ∞, and for all t ∈ R and x, y ∈ R 2 as in Ogunlade et al [26].…”

Section: Existence and Uniqueness For The Stochastic Differentialmentioning

confidence: 99%

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Modeling Cholera Epidemiology Using Stochastic Differential Equations

Iddrisu,

Iddrisu

2023

Journal of Applied Mathematics

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In this study, we extend Codeço’s classical SI-B epidemic and endemic model from a deterministic framework into a stochastic framework. Then, we formulated it as a stochastic differential equation for the number of infectious individuals I t under the role of the aquatic environment. We also proved that this stochastic differential equation (SDE) exists and is unique. The reproduction number, R 0 , was derived for the deterministic model, and qualitative features such as the positivity and invariant region of the solution, the two equilibrium points (disease-free and endemic equilibrium), and stabilities were studied to ensure the biological meaningfulness of the model. Numerical simulations were also carried out for the stochastic differential equation (SDE) model by utilizing the Euler-Maruyama numerical method. The method was used to simulate the sample path of the SI-B stochastic differential equation for the number of infectious individuals I t , and the findings showed that the sample path or trajectory of the stochastic differential equation for the number of infectious individuals I t is continuous but not differentiable and that the SI-B stochastic differential equation model for the number of infectious individuals I t fluctuates inside the solution of the SI-B ordinary differential equation model. Another significant feature of our proposed SDE model is its simplicity.

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Section: Existence and Uniqueness For The Stochastic Differentialmentioning

confidence: 93%

Section: Existence and Uniqueness For The Stochastic Differentialmentioning

confidence: 99%

Modeling Cholera Epidemiology Using Stochastic Differential Equations

Iddrisu,

Iddrisu

2023

Journal of Applied Mathematics

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“…"Many researchers have created mathematical models to explore the dynamics of typhoid fever while considering a variety of control techniques, including vaccine, therapy, and screening". 7 Until 2017, there is no study has been done to investigate typhoid fever dynamics with the application of optimal control methods and cost-effectiveness analysis of the applied control strategies. So, we have worked on this data initially to solve it analytically.…”

Section: Introductionmentioning

confidence: 99%

Semi - Analytical Solution of Modelled Typhoid Fever Disease

Palanivelu

2022

CHCMJ

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To analyze the optimal control of the Typhoid fever virus a mathematical modeling was developed by Getachew Teshome Tilahun. We have approached a Homotopy Perturbation Method to solve a linear differential equation. An analytical solution of Susceptible People(S), Infected People (I), Carrier People (C), Recovered People (R), and Bacteria People ( is obtained and compared with simulation results. A significant agreement is produced when approximate analytical results are compared to numerical simulation. The treatment rate of infectious disease (, Natural death rate (and typhoid-induced death rates (α) are discussed.

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“…Many scholars have developed mathematical models that aim at studying the dynamics of typhoid fevers while incorporating a combination of control strategies, such as vaccination, treatment, and screening [6]. In this study, we investigate the impact of treatment alone in controlling typhoid fever.…”

mentioning

confidence: 99%

Mathematical modeling of the impact of treatment on the dynamics of typhoid

Nyaberi

Musaili

2021

J Egypt Math Soc

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In this paper, we propose a mathematical model for the transmission of typhoid which analyzes the impact of treatment of the infected individuals on the dynamics of the disease. The model consists of human population and pathogen population. The human population is subdivided into three compartments, namely susceptible individuals, infected individuals, and recovered individuals and pathogen population comprises one compartment. We derived the basic reproduction number $${\mathcal {R}}_0$$ R 0 , and analyzed the dynamical behaviors of both disease free equilibrium and endemic equilibrium by the theory of ordinary differential equations. Using MATLAB, we carried out numerical simulation and the findings indicate that effective treatment is adequate in eradicating typhoid fever.

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On the Effect of Vaccination, Screening and Treatment in Controlling Typhoid Fever Spread Dynamics: Deterministic and Stochastic Applications

Cited by 5 publications

References 8 publications

Modeling Cholera Epidemiology Using Stochastic Differential Equations

Modeling Cholera Epidemiology Using Stochastic Differential Equations

Semi - Analytical Solution of Modelled Typhoid Fever Disease

Mathematical modeling of the impact of treatment on the dynamics of typhoid

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