Abstract
We propose and analyze a compartmental nonlinear deterministic mathematical model for the typhoid fever outbreak and optimal control strategies in a community with varying population. The model is studied qualitatively using stability theory of differential equations and the basic reproductive number that represents the epidemic indicator is obtained from the largest eigenvalue of the next-generation matrix. Both local and global asymptotic stability conditions for disease-free and endemic equilibria are determined. The model exhibits a forward transcritical bifurcation and the sensitivity analysis is performed. The optimal control problem is designed by applying Pontryagin maximum principle with three control strategies, namely, the prevention strategy through sanitation, proper hygiene, and vaccination; the treatment strategy through application of appropriate medicine; and the screening of the carriers. The cost functional accounts for the cost involved in prevention, screening, and treatment together with the total number of the infected persons averted. Numerical results for the typhoid outbreak dynamics and its optimal control revealed that a combination of prevention and treatment is the best cost-effective strategy to eradicate the disease.
Highlights
According to [1], “infectious diseases are those diseases caused by viruses, bacteria, epiphytes, and parasites such as protozoans or worms that have a potential to spread into the population .”
“Most of the time typhoid fever is caused by lack of sanitation in which the disease causing bacteria is transmitted by ingestion of contaminated food or water” WHO, 2003
In view of the above, we developed a deterministic mathematical model to investigate the dynamics of typhoid fever with optimal control strategies and we investigated the cost-effectiveness of the implemented control strategies
Summary
According to [1], “infectious diseases are those diseases caused by viruses, bacteria, epiphytes, and parasites such as protozoans or worms that have a potential to spread into the population .” Typhoid fever is one of the common infectious diseases in human beings that is caused by different species of Salmonella. Typhoid fever is one of the common infectious diseases in human beings that is caused by different species of Salmonella. Mathematical models have great benefits for describing the dynamics of infectious disease It plays a significant role in predicting suitable control strategies and analyzing and ranking their cost-effectiveness (for example, see Okosun and Makinde [3,4,5,6,7]). We have identified that till there is no study that has been done to investigate the typhoid fever dynamics with the application of optimal control methods and cost-effectiveness analysis of the applied control strategies. In view of the above, we developed a deterministic mathematical model to investigate the dynamics of typhoid fever with optimal control strategies and we investigated the cost-effectiveness of the implemented control strategies
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