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Alhassan

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Alhassan is a registered researcher in their academic field.

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4 research works linked to this profile

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Research · 2026 · Ktrend - International Journal of Computational Mathematics and Scientific Computing

Mathematical Modelling of the Impact of Dengue Fever Using Nonlinear Differential Equations

Alhassan, J. C.

Dengue fever is a mosquito-borne viral disease that remains a major public health concern in tropical and subtropical regions. This study presents a seven-compartment nonlinear differential equation model comprising four human classes (susceptible, exposed, infectious, and recovered) and three mosquito classes (susceptible, exposed, and infectious) to investigate the transmission dynamics of dengue fever. The model is analysed to establish the non-negativity and boundedness of solutions, determine the biologically feasible region, derive the disease-free equilibrium, and compute the basic reproduction number, $R_0$, using the next-generation matrix method. Local stability analysis of the disease-free equilibrium and the threshold behaviour of the endemic equilibrium are also investigated. The results show that dengue transmission can be eliminated when $R_0<1$, whereas the disease persists when $R_0>1$. The findings emphasize that integrated vector control, environmental sanitation, surveillance, early diagnosis, and effective clinical management are essential for reducing dengue transmission and mitigating future outbreaks.

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ARIMA; Prophet; Markov chain; time series; mathematical modelling; forecasting · 2026 · Ktrend – Nigerian Journal of Mathematical and Computational Sciences

Mathematical Modelling and Forecasting of Inflation Dynamics in Nigeria Using ARIMA, Prophet, and Markov Chain Models

Tombotamunoa W. J. LAWSON, Alhassan, C. J

This study develops and compares three mathematical frameworks for modelling monthly inflation dynamics in Nigeria: an autoregressive integrated moving-average model, a Prophet additive forecasting model, and a finite-state Markov chain. The analysis uses 281 monthly observations of headline inflation covering January 2003 to May 2026. Preliminary tests indicate that the level series is non-stationary, while first differencing produces a stationary process. A systematic information-criterion search selected an ARIMA(2,1,3) model. A twelve-month holdout experiment showed that ARIMA outperformed Prophet, with mean absolute error, root mean squared error, and mean absolute percentage error of 6.69, 7.60, and 41.08%, respectively, compared with 16.16, 16.92, and 95.39% for Prophet. The relatively large errors reflect a major structural discontinuity near the end of the sample and demonstrate the difficulty of extrapolating inflation under changing measurement and macroeconomic regimes. The Markov model classified inflation as low, moderate, or high and revealed strong state persistence, with self-transition probabilities of 0.913, 0.945, and 0.936. Its stationary distribution assigns probabilities of 0.246, 0.586, and 0.168 to the low, moderate, and high regimes. The combined evidence shows that ARIMA is more effective for short-run numerical forecasting, Prophet is useful for decomposable trend-seasonal representation but is vulnerable to abrupt breaks, and the Markov chain provides interpretable regime probabilities. The study recommends ensemble forecasting, explicit structural-break treatment, and periodic model re-estimation for policy-oriented inflation monitoring in Nigeria.

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Malaria; antimalarial drug; nonlinear mathematical model; disease-free equilibrium; basic reproduction number; graphical analysis. · 2026 · African Journal of Mathematics, Statistics and Computer Science

The Impact of Antimalarial Drug on the Dynamics of Malaria Transmission Using Nonlinear Mathematical Model

Alhassan, J. C, F. R. Akerejola

This study presents a nonlinear mathematical model for investigating the impact of antimalarial drug intervention on the transmission dynamics of malaria in a coupled human–mosquito population. The total population is divided into susceptible, exposed, infected, and recovered human compartments together with susceptible, exposed, and infected mosquito compartments. The model preserves the original transmission structure while incorporating the effectiveness of antimalarial drugs as a control parameter influencing the recovery of infected individuals. Qualitative analyses of the model are performed by determining the disease-free equilibrium, endemic equilibrium, and the basic reproduction number, $R_0$, using the next-generation matrix approach. Local asymptotic stability of the disease-free equilibrium is established under the threshold condition $R_01$, the endemic equilibrium becomes feasible and the disease persists within the population. Numerical simulations and graphical analyses are carried out to illustrate the temporal evolution of the human and mosquito compartments under varying levels of antimalarial drug effectiveness. The simulation results demonstrate that increasing treatment effectiveness substantially reduces the infected human and mosquito populations while increasing the recovered population, thereby lowering disease prevalence. Sensitivity analysis further reveals that treatment effectiveness, transmission rates, and mosquito biting rates are among the most influential parameters governing malaria transmission. The findings highlight the critical role of sustained antimalarial drug administration, alongside vector control strategies, in reducing the malaria burden and provide additional quantitative evidence supporting the use of mathematical modelling for evaluating intervention policies and informing public health decision-making.

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Research · 2026 · Ktrend - International Journal of Mathematics and Statistics (IJMS)

A Deterministic Mathematical Model for the Transmission Dynamics of Typhoid Fever Incorporating Asymptomatic Carriers

Robert Folorunsho Akerejola, Michael Nsikan John, ALHASSAN, C.J.

Typhoid fever is a highly infectious disease, and remains a major public health problem, especially in low- and middle-income countries, despite several interventions such as environmental sanitation, personal hygiene, vaccination, and treatment with antibiotic drugs. Evidently, asymptomatic typhoid carriers play a critical role in the transmission dynamics of typhoid fever. Therefore, this research work presents a deterministic mathematical model on the dynamics and spread of typhoid fever incorporating asymptomatic carriers. The basic reproduction number, R0 of the proposed model is computed using the next generation matrix approach, and the stability analyses of the disease-free equilibrium were investigated. Results show that the disease-free equilibrium is locally asymptotically stable when R0 < 1, and globally asymptotically stable when R0 ? 1.

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