Analyzing the dynamic patterns of COVID-19 through nonstandard finite difference scheme

Abstract This paper presents a novel approach to analyzing the dynamics of COVID-19 using nonstandard finite difference (NSFD) schemes. Our model incorporates both asymptomatic and symptomatic infected individuals, allowing for a more comprehensive understanding of the epidemic's spread. We introduce an unconditionally stable NSFD system that eliminates the need for traditional Runge–Kutta methods, ensuring dynamical consistency and numerical accuracy. Through rigorous numerical analysis, we evaluate the performance of different NSFD strategies and validate our analytical findings. Our work demonstrates the benefits of using NSFD schemes for modeling infectious diseases, offering advantages in terms of stability and efficiency. We further illustrate the dynamic behavior of COVID-19 under various conditions using numerical simulations. The results from these simulations demonstrate the effectiveness of the proposed approach in capturing the epidemic's complex dynamics

Asset liability management for the Bank of Uganda defined benefits scheme by stochastic programming

We develop a model for asset liability management of pension funds, which is solved by stochastic programming techniques. Using data provided by the Bank of Uganda Defined Benefits Scheme, which is closed to new members, we obtain the optimal investment policies. Randomly sampled scenario trees using the mean and covariance structure of the return distribution are used for generating the coefficients of the stochastic program. Liabilities are modelled by remaining years of life expectancy and guaranteed period for monthly pension. We obtain the funding situation of the scheme at each stage, and the terminal cash injection by the sponsor required to meet all future benefit payments, in absence of contributing members

Long Term Projection of the Demographic and Financial Evolution of the Parliamentary Pension Scheme of Uganda

We study the Parliamentary Pension Scheme of Uganda, a hybrid cash balance scheme which is contributory. It has two categories of members, the staff of the Parliamentary Commission and the Members of Parliament. A long term projection of the scheme's demographic and financial evolution is done to asses its sustainability and fairness with respect to the two categories of members. The projection of the scheme's future members is done using non-linear regression. The distribution of future members by age states is done by Markov model using frequencies of state transition of the scheme members. We project the future contributions, accumulated funds, benefits, asset and liability values together with associated funding ratios. The results show that the fund is neither sustainable nor fair with respect to the two categories of members. (original abstract

Long term projection of the demographic and financial evolution of the parliamentary pension scheme of Uganda

We study the Parliamentary Pension Scheme of Uganda, a hybrid cash balance scheme which is contributory. It has two categories of members, the staff of the Parliamentary Commission and the Members of Parliament. A long term projection of the schemes demographic and financial evolution is done to asses its sustainability and fairness with respect to the two categories of members. The projection of the schemes future members is done using non-linear regression. The distribution of future members by age states is done by Markov model using frequencies of state transition of the scheme members. We project the future contributions, accumulated funds, benefits, asset and liability values together with associated funding ratios. The results show that the fund is neither sustainable nor fair with respect to the two categories of members.Funding Agencies|Makerere University [316]</p

Exploring local and global stability of COVID-19 through numerical schemes

Abstract Respiratory sensitivity and pneumonia are possible outcomes of the coronavirus (COVID-19). Surface characteristics like temperature and sunshine affect how long the virus survives. This research article analyzes COVID-19 mathematical model behavior based on symptomatic and non-symptomatic individuals. In the reproductive model, the best result indicates the intensity of the epidemic. Our model remained stable at a certain point under controlled conditions after we evaluated a specific element. This approach is in place of traditional approaches such as Euler’s and Runge–Kutta’s. An unusual numerical approach known as the non-standard finite difference (NSFD) scheme is used in this article. This numerical approach gives us positivity. A dependable numerical analysis allowed us to evaluate different approaches and verify our theoretical results. Unlike the widely used Euler and RK4 approaches, we investigated the benefits of implementing NSFD schemes. By numerically simulating COVID-19 in a variety of scenarios, we demonstrated how our theoretical concepts work. The simulation findings support the usefulness of both approaches