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
Periodic forcing is a standard feature of ecological competition models, but the response of a coexistence state is often summarized by numerical trajectories or by a high-frequency approximation. We derive two complementary diagnostics for a two-species Lotka–Volterra competition system with sinusoidal forcing of intrinsic growth rates and constant competition coefficients. First, every positive solution with the forcing period has cycle means exactly equal to the equilibrium of the unforced system; this follows from averaging the per-capita log-growth equations and is independent of forcing amplitude, frequency, and phase. Second, for small forcing, the complex population response is given by a resolvent, $(i\omega I-J)^{-1}$, acting on the species-specific forcing vector, where $J$ is the coexistence Jacobian. This formula predicts amplitudes and phase shifts, including the cross-species effects of competition. Numerical integrations for a positive-coexistence parameter set validate the response formula over a broad frequency range and show strong sensitivity of oscillation amplitude to the relative phase of the two growth cycles, even though cycle means remain fixed. The computed periodic orbit is locally attracting, with both Floquet multipliers inside the unit circle. The contribution is a compact frequency–phase response analysis and a mean-invariance result for a classical periodically forced competition model; it is not a claim that periodic Lotka–Volterra competition is new. The simulations are illustrative and are not fitted to empirical population data.
Tombotamunoa W. J. LAWSON, Eze ChikwemKtrend - International Journal of Computational Mathematics and Scientific Computing · 2026
This paper examines the suborbital graphs generated by the product actions of the wreath products $S_m \wr S_n$, $A_m \wr S_n$, $C_m \wr S_n$, and $D_{2m} \wr S_n$ on the Cartesian power $X^n$. Using permutation group theory, orbit and stabilizer analysis, combinatorial techniques, and computational verification, the study investigates the classification of suborbits and subdegrees and the structural properties of the resulting graphs. The analysis focuses on the pairing properties of orbitals and graph characteristics, including connectivity, vertex degree, regularity, transitivity, girth, and symmetry. The findings reveal how the orbit structure of each base group, together with coordinate permutations, determines the structure of the associated suborbital graphs. In particular, under suitable conditions, the symmetric and alternating group actions yield adjacency structures governed by Hamming distance, whereas the cyclic and dihedral group actions produce graph structures reflecting their respective permutation actions. The study provides a group-theoretic framework for examining suborbital graphs arising from wreath product actions and contributes to the understanding of the relationship between permutation groups, Cartesian powers, and algebraic graph structures.
