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All Journal Communication in Biomathematical Sciences Jambura Journal of Biomathematics (JJBM)
Ebenezer Bonyah
Department of Mathematics Education, Akenten Appiah Menka University of Skills Training and Entrepreneurial Development, Kumasi, Ghana
Computer Science & IT Decision Sciences, Operations Research & Management Mathematics Public Health Social Sciences

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A Malaria Status Model: The Perspective of Mittag-Leffler Function with Stochastic Component Ebenezer Bonyah
Communication in Biomathematical Sciences Vol. 5 No. 1 (2022)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2022.5.1.3

Abstract

Malaria continues to affect many individuals irrespective of the status or class particularly in Sub-Saharan Africa. In this work, an existing malaria status classical model is studied in fractionalized perspective. The positivity and boundedness of the malaria model is studied. The existence and uniqueness of solutions based on fractional derivative and stochastic perspective is established. The numerical simulation results depict that the infectious classes of humans and vector increase as the fractional order derivative increases. Susceptible classes humans and vector reduce as the fractional order derivative increases. This phenomenon is peculiar with epidemiological models. The implications of the results are that in managing the dynamics of the status model, the fractional order derivative as well as its associated operator is important. It is observed that fractional order derivative based on Mittag-Leffler function provides a better prediction because of its crossover property, its non-local and non-singular property.
Critical waves in a nonlocal dispersion delayed susceptible-infected-confined-quarantined-recovered outbreak model with general incidence function Nidhal Ali; Rassim Darazirar; Sawsan Abed; Ahmed Mohsen; Ebenezer Bonyah
Jambura Journal of Biomathematics (JJBM) Vol. 7 No. 1: March 2026
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v7i1.15

Abstract

We study a delayed nonlocal epidemic model that includes the effects of confinement and a generalized incidence function. The model takes into account the spatial movements of the population through a nonlocal dispersal kernel and the behavioral control through a confinement parameter. First, we calculate the basic reproduction number $R_0$ and show its explicit dependence on the confinement rate. Second, we determine the minimal wave speed $\zeta^*$ of traveling wave solutions connecting the disease-free equilibrium to the endemic equilibrium. We show that $\zeta^*$ is given by the principal root of the corresponding characteristic equation and that (i) no traveling wave exists for $\zeta<\zeta^*$, and (ii) traveling waves exist for all $\zeta>\zeta^*$. Moreover, we show that the minimal wave speed is a monotone decreasing function of the confinement rate. Our results are obtained through a combination of spectral theory, upper-lower solution methods, and monotone iteration schemes that are modified to account for the joint effects of delay and nonlocal dispersal. Numerical simulations confirm the analytical prediction of the minimal wave speed and illustrate the quantitative slowing effect induced by confinement. These results provide a rigorous mathematical characterization of how mobility, delay, and confinement jointly determine epidemic invasion and spatial propagation.
Co-Authors Ahmed Mohsen Nidhal Ali Rassim Darazirar Sawsan Abed