DEVELOPMENT OF DETERMINISTIC MODELS OF TYPHOID FEVER WITH PREVENTION AND CONTROL STRATEGIES
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Date
2021-04
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UNIVERSITY OF ILORIN
Abstract
Typhoid fever is a serious bacterial infection caused by Salmonella typhi. Typhoid fever is usually contracted by the ingestion of water or food contaminated with urine or faeces of infected carriers and is, therefore, common in areas with poor sanitation. In developing countries, refugee camps and crowded areas, typhoid fever outbreaks are frequent. In most existing literature on typhoid fever models, the effects of human to human and environment to human transmission of typhoid fever are not properly addressed, this study therefore aimed at extending the existing typhoid fever models to address the effects of some control strategies (educational campaign and vaccination) on human to human and environment to human transmission in typhoid fever prone communities. The objectives were to (i) obtain the existence, uniqueness and positivity solution of all the models; ( ii ) derive the disease free and endemic equilibra that govern the spread of typhoid fever; (iii) perform a sensitivity analysis of the models; (iv) determine the optimal strategy for implementing combine control strategies. The method employed included the application of Next Generational Matrix (NGM) technique to obtain the basic reproduction number, local and global stability analyses of the models using Lyapunov function and Lasalle’s invariance principle, series solutions of the models by using Differential Transform Method (DTM) and
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Variational Iteration Method (VIM), optimal control analysis to establish the conditions necessary for eradication of the disease. The findings of the study were that:
(i) the existence, uniqueness and positivity solutions of all the models established that the models were well posed;
(ii) the disease free and endemic equilibra that govern the spread of typhoid fever were found to be stable;
(iii) the most sensitive parameter to typhoid fever management was education; and
(iv) control strategies become more effective when vaccination and educational campaign program are combined, prevention methods become more effective in preventing the disease transmission.
The study concluded that possible optimal control strategies become more effective in the control and elimination of typhoid fever when vaccination and educational campaign are combined. Since educational campaign was the most sensitive to typhoid fever management, it is therefore recommended that any measure directed towards achieving typhoid fever-free society should include educational campaign.
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Keywords
DETERMINISTIC MODELS, TYPHOID FEVER, PREVENTION, CONTROL STRATEGIES