Browsing by Author "Arthur, Yarhands Dissou"

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    Fractal–fractional age-structure study of omicron SARS-CoV-2 variant transmission dynamics
    (Elsevier, 2022-09) Addai, Emmanuel; Zhang, Lingling; Asamoah, Joshua Kiddy K.; Preko, Ama Kyerewaa; Arthur, Yarhands Dissou; 0000-0002-7066-246X
    This paper proposes a new fractal–fractional age-structure model for the omicron SARS-CoV-2 variant under the Caputo–Fabrizio fractional order derivative. Caputo–Fabrizio fractal–fractional order is particularly successful in modelling real-world phenomena due to its repeated memory effect and ability to capture the exponentially decreasing impact of disease transmission dynamics. We consider two age groups, the first of which has a population under 50 and the second of a population beyond 50. Our results show that at a population dynamics level, there is a high infection and recovery of omicron SARS-CoV-2 variant infection among the population under 50 (Group-1), while a high infection rate and low recovery of omicron SARS-CoV-2 variant infection among the population beyond 50 (Group-2) when the fractal–fractional order is varied.
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    Non-fractional and fractional mathematical analysis and simulations for Q fever
    (Elsevier, 2022-01) Asamoah, Joshua Kiddy K.; Okyere, Eric; Yankson, Ernest; Opoku, Alex Akwasi; Adom-Konadu, Agnes; Acheampong, Edward; Arthur, Yarhands Dissou; 0000-0002-7066-246X
    The purpose of analysing the transmission dynamism of Q fever (Coxiellosis) in livestock and incorpo- rating ticks is to outline some management practices to minimise the spread of the disease in livestock. Ticks pass coxiellosis from an infected to a susceptible animal through a bite. The faecal matter can also contain coxiellosis, thus contaminating the environment and spreading the disease. First, a nonlinear integer order mathematical model is developed to represent the spread of this infectious disease in live- stock. The proposed integer model investigates the positivity and boundedness, disease equilibria, basic reproduction number, bifurcation, and sensitivity analysis. Through mathematical analysis and numerical simulations, it shows that if the environmental transmission and the effective shedding rate of coxiella burnetii into the environment by both asymptomatic and symptomatic livestock are zero, then the usual threshold hold and it produces forward bifurcation. It is noticed that an increase in the recruitment rate of ticks produces backward bifurcation. And also, it is seen that an increase in the natural decay rate of the bacterial in the environment reduces the backward bifurcation point. Furthermore, to take care of the memory aspect of ticks on their host, we modified the initially proposed integer order model by introducing Caputo, Caputo-Fabrizio, Atangana-Baleanu fractional differential operators. The existence and uniqueness of these three newly developed fractional-order differential models are shown using the Banach fixed point theorem. Numerical trajectories are obtained for each of the fractional-order math- ematical models. The trajectory of some fractional orders converges to the same endemic equilibrium point as the integer order. Finally, it is seen that the Atangana-Baleanu fractional differential operator captures more susceptibilities and fewer infections than the other operators.