Spatial and age-dependent population dynamics model with an additional structure: can there be a unique solution?

A simple age-dependent population dynamics model with an additional structure or physiological variable is presented in its variational formulation. Although the model is well-posed, the closed form solution with space variable is difficult to obtain explicitly, we prove the uniqueness of its solutions using the fundamental Green’s formula. The space variable is taken into account in the extended model with the assumption that the coefficient of diffusivity is unity

An Age-structured Resource-Consumer Dynamical Model

Many dynamical systems in population biology in which agents compete for resources may exhibit chaotic fluctuations. This short letter develops Gamarra and Solé\u27s previous work. We briefly review a classical model of population with complex dynamics, and proceed to study the dynamics of an age-structured resource-consumer model, in which the fertility coefficients are density independent. Implicit or first integral solutions of the model are obtained, and conditions for which they are stable given. It is observed that resource availability at any time depends on the number of potential consumers present

A Partially Discretized Age-Dependent Population Model with an Additional Stucture

A semi-discretization method for solving an age-dependent population dynamics model with an additional structure is proposed. This method, unlike previous ones, considers the partial discretization which reduces the model equation into a first order ordinary differential equation. The latter is then solved explicitly and conditions under which second order accuracy arises are given. While the approach adopted is basically analytical, the main result shows that the sum of errors is bounded. An extension to the non-trivial case where growth depends on the additional parameter leads to a Riccati equation, and the existence andconvergence of solutions are proved

Asymptotic Stability of an Abstract Delay Functional-Differential Equation

We study the exponential asymptotic stability of an abstract functional-differential equation with a mixed type of deviating arguments, namely: c which might represent the gestation period of the population and r(u(t)), a suitably defined function. The equation is reduced to its equivalent integral form and solved via Laplace transform method. An interesting connection of our study is with generalizations of populations with potentially complex (chaotic) dynamics

Private sector costing of voluntary medical male circumcision in South Africa

In 2010, after voluntary medical male circumcision (VMMC) had been shown to be one of the most cost-effective strategies for preventing HIV infections, South Africa initiated a VMMC program with an ambitious target of performing 4.3 million circumcisions by 2016. However, because of a gap in knowledge concerning the overall cost of scaling up services, the South African National Department of Health requested that Project SOAR—Supporting Operational AIDS Research—conduct a private-sector costing of providing VMMC services in South Africa. The findings presented in this report provide a detailed investigation, through a comprehensive bottom-up approach, of the costs to private providers in offering VMMC to clients. Results from this study could inform discussion with private insurance providers in South Africa about standardization of VMMC tariffs. It also provides a strong rationale for reimbursing private sector providers for circumcisions of uninsured clients

Time-delayed SIS epidemic model with population awareness

This paper analyses the dynamics of infectious disease with a concurrent spread of disease awareness. The model includes local awareness due to contacts with aware individuals, as well as global awareness due to reported cases of infection and awareness campaigns. We investigate the effects of time delay in response of unaware individuals to available information on the epidemic dynamics by establishing conditions for the Hopf bifurcation of the endemic steady state of the model. Analytical results are supported by numerical bifurcation analysis and simulations

Optimal (Control of) Intervention Strategies for Malaria Epidemic in Karonga District, Malawi

Malaria is a public health problem for more than 2 billion people globally. About 219 million cases of malaria occur worldwide and 660,000 people die, mostly (91%) in the African Region despite decades of efforts to control the disease. Although the disease is preventable, it is life-threatening and parasitically transmitted by the bite of the female Anopheles mosquito. A deterministic mathematical model with intervention strategies is developed in order to investigate the effectiveness and optimal control strategies of indoor residual spraying (IRS), insecticide treated nets (ITNs) and treatment on the transmission dynamics of malaria in Karonga District, Malawi. The effective reproduction number is analytically computed, and the existence and stability conditions of the equilibria are explored. The model does not exhibit backward bifurcation. Pontryagin’s Maximum Principle which uses both the Lagrangian and Hamiltonian principles with respect to a time dependent constant is used to derive the necessary conditions for the optimal control of the disease. Numerical simulations indicate that the prevention strategies lead to the reduction of both the mosquito population and infected human individuals. Effective treatment consolidates the prevention strategies. Thus, malaria can be eradicated in Karonga District by concurrently applying vector control via ITNs and IRS complemented with timely treatment of infected people

Using HIV self-testing to increase the affordability of community-based HIV testing services.

OBJECTIVES: This study estimates the costs of community-based HIV testing services (HTS) in Lesotho and assesses the potential efficiency gains achieved by adding HIV self-testing (HIVST) and then self-testing booths. DESIGN: Micro-costing analysis using longitudinal data from a real-world intervention. METHODS: We collected data prospectively on provider's costs and programmatic outcomes over three time periods of approximately 8 months each, between May 2017 and April 2019. The scope of services was extended during each period as follows: HTS only, HTS and HIVST, HTS and HIVST with individual HIVST booths wherein clients were encouraged to self-test on-site followed by on-site confirmative testing for those with reactive self-test. For each implementation period, we estimated the full financial and economic implementation costs, the incremental costs of adding HIVST onto conventional HTS and the cost per HIV positive case identified. RESULTS: Costs per HIV-positive case identified increased between period 1 (US$956) and period 2 (US$1249) then dropped in period 3 (US$813). Full versus incremental cost analyses resulted in large differences in the magnitude of costs, attributable to methods rather than resource use: for example, in period 3, the average full and incremental cost estimates for HTS were US$34.3 and US$23.5 per person tested, and for HIVST were US$37.7 and US$14.0 per kit provided, respectively. CONCLUSION: In Lesotho, adding HIVST to community-based HTS improves its overall affordability for HIV-positive case finding. The reporting of both full and incremental cost estimates increase transparency for use in priority setting, budgeting and financial planning for scale-up