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.

We propose and analyse a nonlinear mathematical model for the transmission dynamics of pneumonia disease in a population of varying size. The deterministic compartmental model is studied using stability theory of differential equations. The effective reproduction number is obtained and also the asymptotic stability conditions for the disease free and as well as for the endemic equilibria are established. The possibility of bifurcation of the model and the sensitivity indices of the basic reproduction number to the key parameters are determined. Using Pontryagin's maximum principle, the optimal control problem is formulated with three control strategies: namely disease prevention through education, treatment and screening. The cost-effectiveness analysis of the adopted control strategies revealed that the combination of prevention and treatment is the most cost-effective intervention strategies to combat the pneumonia pandemic. Numerical simulation is performed and pertinent results are displayed graphically.

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An asymptotic unfolding of a dynamical system near a rest point is a system with additional parameters, such that every oneparameter deformation of the original system can be embedded in the unfolding preserving all properties that can be detected by asymptotic methods. Asymptotic unfoldings are computed using normal (and hypernormal) form methods. We present a simplified and improved method of computing such unfoldings that can be used in any normal form style.

Most hosts harbor multiple pathogens at the same time in disease epidemiology. Multiple pathogens have the potential for interaction resulting in negative impacts on host fitness or alterations in pathogen transmission dynamics. In this paper we develop a mathematical model describing the dynamics of HIV-malaria coinfection. Additionally, we extended our model to examine the role treatment (of malaria and HIV) plays in altering populations' dynamics. Our model consists of 13 interlinked equations which allow us to explore multiple aspects of HIV-malaria transmission and treatment. We perform qualitative analysis of the model that includes positivity and boundedness of solutions. Furthermore, we evaluate the reproductive numbers corresponding to the submodels and investigate the long term behavior of the submodels. We also consider the qualitative dynamics of the full model. Sensitivity analysis is done to determine the impact of some chosen parameters on the dynamics of malaria. Finally, numerical simulations illustrate the potential impact of the treatment scenarios and confirm our analytical results.