Kazeem A. Tijani, Chinwendu E. Madubueze, Reuben I. Gweryina
{"title":"Modelling Typhoid Fever Transmission with Treatment Relapse Response: Optimal Control and Cost-Effectiveness Analysis","authors":"Kazeem A. Tijani, Chinwendu E. Madubueze, Reuben I. Gweryina","doi":"10.1134/s2070048224700169","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Typhoid fever has become a public health concern, especially in developing countries where sanitation and personal hygiene are not taken seriously, coupled with the non-availability of safe drinking water. Despite the antibiotic treatment, about 2–5% of recovered humans still harbour the typhoid bacteria in their bodies and shed it via their faeces in the population, making it difficult to eradicate the disease. Thus, the effect of limited clinical efficacy of the antibiotics with corresponding relapse response to treatment on infected humans is examined in this paper by formulating a deterministic mathematical model for direct and indirect transmission mode of Typhoid infection. The basic reproduction number is analytically derived and used to implement the global sensitivity analysis of the model’s parameters that employed Latin hypercube Sampling (LHS) with Partial Rank Correlation Coefficient (PRCC). Regarding the sensitivity analysis result, the optimal control and cost-effectiveness analysis are analysed and simulated numerically with four controls, the water, sanitation and hygiene (WASH) practice and awareness campaign control, the sterilisation and disinfection control, the potency of antibiotics control and the screening control. The optimal control analysis applied Pontrygin’s maximum principle to the optimal control problem. The limited efficacy of antibiotics with corresponding relapse response to treatment is shown to influence the spread of typhoid infection in the population. Furthermore, the cost-effectiveness analysis employed Infected Averted Ratio (IAR), Average Cost-effectiveness Ratio (ACER) and Increment Cost-effectiveness Ratio (ICER) techniques to four cases (I–IV) that compared fifteen strategies. The results indicate that the WASH practice and awareness campaign (Strategy 1) is good to implement for single control implementation, while for double control implementation, the WASH practice and awareness campaign and the potency of antibiotics administered to typhoid patients (Strategy 6) is the best to consider. Combining Strategy 6 and screening control is the most cost-effective for triple controls. Furthermore, the overall computation of cost-effectiveness among all the most cost-effective with all the controls combined suggests that Strategy 1 is the most cost-effective strategy to implement for eradicating typhoid infection in the population.</p>","PeriodicalId":38050,"journal":{"name":"Mathematical Models and Computer Simulations","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Models and Computer Simulations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s2070048224700169","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
Typhoid fever has become a public health concern, especially in developing countries where sanitation and personal hygiene are not taken seriously, coupled with the non-availability of safe drinking water. Despite the antibiotic treatment, about 2–5% of recovered humans still harbour the typhoid bacteria in their bodies and shed it via their faeces in the population, making it difficult to eradicate the disease. Thus, the effect of limited clinical efficacy of the antibiotics with corresponding relapse response to treatment on infected humans is examined in this paper by formulating a deterministic mathematical model for direct and indirect transmission mode of Typhoid infection. The basic reproduction number is analytically derived and used to implement the global sensitivity analysis of the model’s parameters that employed Latin hypercube Sampling (LHS) with Partial Rank Correlation Coefficient (PRCC). Regarding the sensitivity analysis result, the optimal control and cost-effectiveness analysis are analysed and simulated numerically with four controls, the water, sanitation and hygiene (WASH) practice and awareness campaign control, the sterilisation and disinfection control, the potency of antibiotics control and the screening control. The optimal control analysis applied Pontrygin’s maximum principle to the optimal control problem. The limited efficacy of antibiotics with corresponding relapse response to treatment is shown to influence the spread of typhoid infection in the population. Furthermore, the cost-effectiveness analysis employed Infected Averted Ratio (IAR), Average Cost-effectiveness Ratio (ACER) and Increment Cost-effectiveness Ratio (ICER) techniques to four cases (I–IV) that compared fifteen strategies. The results indicate that the WASH practice and awareness campaign (Strategy 1) is good to implement for single control implementation, while for double control implementation, the WASH practice and awareness campaign and the potency of antibiotics administered to typhoid patients (Strategy 6) is the best to consider. Combining Strategy 6 and screening control is the most cost-effective for triple controls. Furthermore, the overall computation of cost-effectiveness among all the most cost-effective with all the controls combined suggests that Strategy 1 is the most cost-effective strategy to implement for eradicating typhoid infection in the population.
期刊介绍：
Mathematical Models and Computer Simulations is a journal that publishes high-quality and original articles at the forefront of development of mathematical models, numerical methods, computer-assisted studies in science and engineering with the potential for impact across the sciences, and construction of massively parallel codes for supercomputers. The problem-oriented papers are devoted to various problems including industrial mathematics, numerical simulation in multiscale and multiphysics, materials science, chemistry, economics, social, and life sciences.
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