modeled the impact of a 1-time booster of all adults 18 to 64 years of age without consideration of decennial boosters. Our analysis focused on vaccination of a single adult cohort with repeated boosters every 10 years. We believe both strategies are reasonable to consider in modeling exercises and that differences are to be expected given the different strategies considered and the different estimates for incidence used in each model.We agree that herd immunity is a very important consideration. In our sensitivity analysis for herd immunity, we assumed that adult immunization would protect infants too young to be immunized, although we did not assume that unvaccinated adults would receive indirect protection because of other adults being vaccinated. Very scant data exist to support quantitative assumptions about the amount of indirect protection that unvaccinated infants or adults might receive. We chose the analysis without herd immunity as the base case analysis to focus on a pertussis vaccination program's direct benefits to those who would be vaccinated.We agree with Caro and colleagues that the incidence of disease is key to the economic results regardless of the model that is considered. It is clear that if adult disease incidence is similar to adolescent disease incidence, strategies that include adult vaccination will look much more cost-effective. The key factor to consider is the incidence of disease in adults rather than the adolescent/adult ratio for either incidence or utilities. Using utilities to derive the cost per quality-adjusted life-year saved gives both adult and adolescent vaccination strategies appropriate credit for preventing morbidity.We did not perform a mutually exclusive comparison as suggested by Caro and colleagues. The strategies in the model included an adolescent-only, adult-only, and adolescent ϩ adult strategies. In our baseline analysis, the adolescent ϩ adult vaccination strategy was not found to be cost-effective. However, in our sensitivity analyses, it is clear that if adult incidence is high enough and vaccine cost is low enough, adolescent ϩ adult vaccination strategies are reasonably cost-effective. We agree with their statement that the results of our analysis should not preclude additional review of targeted or routine adult vaccination strategies. Models such as ours serve to clarify the issues in public health policy, but a single model rarely provides the final answer to any question. Future studies to refine our understanding of the benefits and costs of pertussis vaccination programs should be conducted as more information is put forward about pertussis vaccine efficacy in adults, disease incidence in adults, vaccine costs, and overall estimates of herd immunity.Up to 15% of patients with hepatitis C do not have an identifiable risk factor. Body piercing has become increasingly popular among high school-and college-aged students (13-25 years), with a prevalence of 25% to 35%. We report the case of a 17-year-old woman with chronic hepatitis C and no identifiable ...
Malaria is one of the major causes of deaths and ill health in endemic regions of sub-Saharan Africa and beyond despite efforts made to prevent and control its spread. Epidemiological models on how malaria is spread have made a substantial contribution on the understanding of disease changing aspects. Previous researchers have used Susceptible -Exposed-Infectious-Recovered (SEIR) model to explain how malaria is spread using ordinary differential equations. In this paper we develop mathematical SEIR model to define the dynamics of the spread of malaria using Delay differential equations with four control measures such as long lasting treated insecticides bed nets, intermittent preventive treatment of malaria in pregnant women (IPTP), intermittent preventive treatment of malaria in infancy (IPTI) and indoor residual spraying. The model is analyzed and reproduction number derived using next generation matrix method and its stability is checked by Jacobean matrix. Positivity of solutions and boundedness of the model is proved. We show that the disease free equilibrium is locally asymptotically stable if R 0 <1 (R 0 -reproduction number) and is unstable if R 0 >1. Numerical simulation shows that, with proper treatment and control measures put in place the disease is controlled.
The Navier-Stokes (N-S) equations for incompressible fluid flow comprise of a system of four nonlinear equations with five flow fields such as pressure P, density ρ and three velocity components u, v, and w. The system of equations is generally complex due to the fact that it is nonlinear and a mixture of the three classes of partial differential equations (PDEs) each with distinct solution methods. The N-S equations fully describe the unsteady fluid flow behaviour of laminar and turbulent types. Previous studies have shown existence of general solutions of fluid flow models but little has been done on numerical solution for velocity of flow in N-S equation of incompressible fluid flow by Crank-Nicolson implicit scheme. In practice, real fluid flows are compressible due to the inevitable variations in density caused by temperature changes and other physical factors. Numerical approximations of the general system of Navier-Stokes equations were made to develop numerical solution model for incompressible fluid flow. Adequate solutions of the latter produce numerical solutions applicable in numerical simulation of fluid flows useful in engineering and science. Non-dimensionalization of variables involved was done. Crank-Nicolson (C.N) implicit scheme was implemented to discretize partial derivatives and appropriate approximation made at the boundaries yielded a linear system of N-S equations model. The linear numerical system was then expressed in matrix form for computation of velocity field by Computational fluid dynamics (CFD) approach using MATLAB software. Numerical results for velocity field in two dimensional space, u(x,y,t) and v(x,y,t) generated in uniform 32×32 grids points of the square flow domains, 0≤x≤1.0 and 0≤y≤1.0 were presented in three dimensional figures. Results showed that the velocity in two dimensional space does not change suddenly for any change in spatial levels, x and y. Therefore, C-N implicit Scheme applied to solve the N-S equations for fluid flow is consistent.
Numerous models of mathematics have existed to pronounce the immunological response to contagion by human immunodeficiency virus (HIV-1). The models have been used to envisage the regression of HIV-1 in vitro and in vivo dynamics. Ordinarily the studies have been on the interface of HIV virions, CD4+T-cells and Antiretroviral (ARV). In this study, time delay, chemotherapy and role of CD8+T-cells is considered in the HIV-1 in-vivo dynamics. The delay is used to account for the latent time that elapses between exposure of a host cell to HIV-1 and the production of contagious virus from the host cell. This is the period needed to cause HIV-1 to replicate within the host cell in adequate number to become transmittable. Chemotherapy is by use of combination of Reverse transcriptase inhibitor and Protease inhibitor. CD8+T-cells is innate immune response. The model has six variables: Healthy CD4+T-cells, Sick CD4+T-cells, Infectious virus, Noninfectious virus, used CD8+T-cells and unused CD8+T-cells. Positivity and boundedness of the solutions to the model equations is proved. In addition, Reproduction number (R 0 ) is derived from Next Generation Matrix approach. The stability of disease free equilibrium is checked by use of linearization of the model equation. We show that the Disease Free Equilibrium is locally stable if and only if R 0 <1 and unstable otherwise. Of significance is the effect of CD8+ T-cells, time delay and drug efficacy on stability of Disease Free Equilibrium (DFE). From analytical results it is evident that for all τ > 0, Disease Free Equilibrium is stable when τ =0.67. This stability is only achieved if drug efficacy is administered. The results show that when drug efficacy of α 1 =0.723 and α 2 =0.723 the DFE is achieved.
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