Terrorism, banditry and kidnapping, here called the triple security threat, have become a central obstacle to stability and sustainable development in Nigeria. This paper reviews the concept, causes and existing mathematical models of these threats. We find that the modelling literature is small and almost entirely deterministic, built on systems of ordinary differential equations whose solutions are fixed once parameters and initial conditions are fixed. Security incidents, by contrast, are discrete, rare, clustered and driven by unpredictable human decisions, so a deterministic model can be misleading: it cannot express the chance that a criminal network dies out by itself or flares up despite control. We survey six classical stochastic processes (Markov chain, Wiener process, random walk, Poisson process, Bernoulli process and queueing models) and assess their fitness for security-threat modelling. Using the kidnapping model of Okrinya and Charles [24] as a worked case, we show how its deterministic threshold maps onto a continuous-time Markov chain and a stochastic differential equation, and how a branching-process approximation yields a probability of kidnapping extinction even when the basic reproduction number exceeds one. We close with four research gaps and a research agenda: an easy-to-use stochastic model, its implementation with pseudo-random and survey data in an intuitionistic fuzzy framework, and an efficient computational procedure.
Timinibife N. Charles, Dickson E. A. Omorogbe, Aniayam B. OkrinyaKtrend - International Journal of Computational Mathematics and Scientific Computing · 2026
Prediction of stock prices is regarded as a difficult task due to its random-walk characteristics. Also, the problem of estimating unobserved latent variables from observed data often arises in stock price prediction. The concept of the Kalman filter serves as a key method used for estimating unobserved variables from observed variables because of its real-time dynamic tracking characteristics. In this work, we investigate the effect of incorporating control input into the Kalman Filter (KF) algorithm for stock price prediction. The KF algorithm was used to predict stock prices by estimating the stock’s hidden state based on noisy observations taking into account the control input. The control input as used in this work is the effective interest rate. The control input was incorporated in the algorithm, to monitor its effect on the stock price prediction. The predicted estimates from the stock price data were evaluated using three evaluation metrics, the Relative Error (RE), Mean Square Error (MSE) and Root Mean Square Error (RMSE). The datasets used are stock prices from First Bank of Nigeria (FBN) and Microsoft Corporation (MSFT) for a one-year period, from August 2024 to September 2025. Numerical simulations were carried out using the MATLAB software. The results showed little increase in the stock prices as a result of the control input. The simulations for the evaluation metrics showed that the FBN stock price could be controlled with an error below 4% and MSFT with an error below 3%. Also, the metrics $\mathrm{MSE}_c$ and $\mathrm{RMSE}_c$ were lower for the FBN and MSFT stock price data. This implies that incorporating control input into the KF algorithm improved estimation accuracy. The study showcases the potential of the Kalman filter as a valuable tool for stock price prediction with control input.
Joy Ijeoma UWAKWE, Felix Noyanim NWOBIKtrend - International Journal of Mathematics and Statistics (IJMS) · 2026
In this research, a stochastic model is developed and analysed for the age structured deterministic model of diphtheria infection. The model includes specific epidemiological classes such as $S_{1}$ Susceptible infant at time $t$ (0-1years), $S_{2}$, Susceptible school children population at time $t$, $V$, Vaccinated population at time $t$, $E$, Exposed population at time $t$, $I_{1}$, Asymptomatic infected population at time $t$, $I_{2}$, symptomatic infected population at time $t$, $I_{D}$, Detected infectious humans at time $t$ (Asymptomatic and symptomatic) population through testing, and $R$, Recovered population at time $t$. The work investigates the transformation of age-structured deterministic model of diphtheria infection into an age-structured stochastic model of diphtheria infection, by applying the well established procedure proposed in [1] and also investigates the existence and uniqueness of solution of the transformed stochastic model. It is established that developed stochastic model of diphtheria infection dynamics satisfies the condition for the existence and uniqueness of solution. The numerical simulation of the work shows that increased vaccination rate will lead to Diphtheria infection extinction while low vaccination rate will produce an epidemic, demonstrates how randomness can cause the outbreak of Diphtheria die out and indicates the effect of random noise in detecting the disease hence suppressing the initial infection wave.
Enobong E. Joshua, Ekere S. Udofia, Blessing I. IsraelKtrend - International Journal of Mathematics and Statistics (IJMS) · 2026
