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

Nyaberi, H. O.; Musaili, Jane S.

doi:10.1186/s42787-021-00125-8

Cited by 7 publications

(5 citation statements)

References 7 publications

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“…The mathematical model for typhoid disease was developed by considering various interventions to control the disease and reduce infection risk. The intervention used most in controlling the disease is treatment [3,18,43,47,50,53,55,57]. Based on some research, treatment is confirmed as the best intervention in controlling the spread of typhoid disease.…”

Section: Systematic Literature Review Resultsmentioning

confidence: 99%

“…The basic compartmental mathematical models to describe the spread of disease are introduced [15][16][17]. The latest mathematical models have involved some factors in the typhoid disease spread, such as treatment in an effort on the infected population [18,19] and the existence of flies as a disease carrier vector that spreads the bacteria Salmonella on food [20]. Moreover, some researchers developed a non-autonomous mathematical model [8,21] to study typhoid transmission by considering the effect of seasonal conditions and some time-dependent parameters.…”

Section: Introductionmentioning

confidence: 99%

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Mathematical Models for Typhoid Disease Transmission: A Systematic Literature Review

2022

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Explaining all published articles on the typhoid disease transmission model was carried out. It has been conducted to understand how Salmonella is transmitted among humans and vectors with variation interventions to control the spread of the typhoid disease. Specific objectives were to (1) identify the model developed, (2) describe the studies, and (3) identify the interventions of the model. It systemically searched and reviewed Dimension, Scopus, and ScienceDirect databases from 2013 through to 2022 for articles that studied the spread of typhoid fever through a compartmental mathematical model. This study obtained 111 unique articles from three databases, resulting in 23 articles corresponding to the created terms. All the articles were elaborated on to identify their identities for more explanation. Various interventions were considered in the model of each article, are identified, and then summarized to find out the opportunities for model development in future works. The whole article’s content was identified and outlined regarding how mathematics plays a role in model analysis and study of typhoid disease spread with various interventions. The study of mathematical modeling for typhoid disease transmission can be developed on analysis and creating the model with direct and indirect interventions to the human population for further work.

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Section: Systematic Literature Review Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mathematical Models for Typhoid Disease Transmission: A Systematic Literature Review

2022

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“…We carry out numerical simulations of the model (1), using MATLAB ode45 solver as carried out in [15]. The parameter values used are presented in Table 1, and the initial populations are taken to be S 0 = 10000, E k 0 = 2000, I k 0 = 100, P k 0 = 1600, and R 0 = 1000.…”

Section: Numerical Simulationmentioning

confidence: 99%

A Mathematical Model of the Dynamics of Coffee Berry Disease

Nyaberi,

Mutuku,

Malonza

et al. 2023

Journal of Applied Mathematics

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Coffee berry disease (CBD) is a fungal disease caused by Colletotrichum kahawae. CBD is a major constraint to coffee production to Kenya and Africa at large. In this research paper, we formulate a mathematical model of the dynamics of the coffee berry disease. The model consists of coffee plant population in a plantation and Colletotrichum kahawae pathogen population. We derived the basic reproduction number R k 0 , and analyzed the dynamical behaviors of both disease-free equilibrium and endemic equilibrium by the theory of ordinary differential equations. Using the MATLAB ode45 solver, we carried out numerical simulation, and the findings are consistent with the theoretical results.

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“…The local and global stability of equilibrium points is also studied 8 . A mathematical model for the transmission of typhoid was developed by Nyaberi and Musaili, and it examines the effects of treatment on the dynamics of the illness 9 . Birger et al studied mathematical models of typhoid transmission by considering FQNS and multidrug resistance separately.…”

Section: Introductionmentioning

confidence: 99%

Numerical investigation of a typhoid disease model in fuzzy environment

Dayan,

Ahmed,

Ali

et al. 2023

Sci Rep

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Salmonella Typhi, a bacteria, is responsible for typhoid fever, a potentially dangerous infection. Typhoid fever affects a large number of people each year, estimated to be between 11 and 20 million, resulting in a high mortality rate of 128,000 to 161,000 deaths. This research investigates a robust numerical analytic strategy for typhoid fever that takes infection protection into consideration and incorporates fuzzy parameters. The use of fuzzy parameters acknowledges the variation in parameter values among individuals in the population, which leads to uncertainties. Because of their diverse histories, different age groups within this community may exhibit distinct customs, habits, and levels of resistance. Fuzzy theory appears as the most appropriate instrument for dealing with these uncertainty. With this in mind, a model of typhoid fever featuring fuzzy parameters is thoroughly examined. Two numerical techniques are developed within a fuzzy framework to address this model. We employ the non-standard finite difference (NSFD) scheme, which ensures the preservation of essential properties like dynamic consistency and positivity. Additionally, we conduct numerical simulations to illustrate the practical applicability of the developed technique. In contrast to many classical methods commonly found in the literature, the proposed approach exhibits unconditional convergence, solidifying its status as a dependable tool for investigating the dynamics of typhoid disease.

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

Cited by 7 publications

References 7 publications

Mathematical Models for Typhoid Disease Transmission: A Systematic Literature Review

Mathematical Models for Typhoid Disease Transmission: A Systematic Literature Review

A Mathematical Model of the Dynamics of Coffee Berry Disease

Numerical investigation of a typhoid disease model in fuzzy environment

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