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Conference Proceedings This Community features the proceedings of conferences hosted by the KNUST or other bodies but had staff from KNUST attending and making presentationsJournal of Science and Technology (JUST) Research Articles from the members of KNUST submitted to the JUSTKumasi Center for Collaborative Research (KCCR) Research Articles Speeches A collection of speeches delivered by the Vice Chancellors and Official visitors to the KNUST
Recent Submissions
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Threshold quantities and Lyapunov functions for ordinary differential equations epidemic models with mass action and standard incidence functions
(Elsevier, 2023-03) Seidu, Baba; Makinde, Oluwole D.; Asamoah, Joshua Kiddy K.; 0000-0002-7066-246X
This paper presents a novel algebraic method for the construction of Lyapunov functions to study global stability of the disease-free equilibrium points of deterministic epidemic ordinary differential equation models with mass action and standard incidence functions. The method is named as Jacobian-Determinant method. In our method, a direct algebraic procedure that also relies only on determinant of the Jacobian matrix of the infected subsystem is developed to determine a threshold quantity, ′ 0 akin to the basic reproduction number, 0 of such class of models. The developed technique is applied on a wide variety of models to construct Lyapunov functions to study the global stability of the infection-free critical points. Further, implementation of our method reveals that the threshold quantity is the same as (or the square) of the basic reproduction
numbers as obtained using the next-generation matrix method. It is further observed that even for models that do not use the standard or mass action incidence, the threshold quantity is still related to the basic reproduction numbers as obtained with the next-generation matrix method.
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Fractional Caputo and sensitivity heat map for a gonorrhea transmission model in a sex structured population
(Elsevier, 2023-09) Asamoah, Joshua Kiddy K.; Sun, Gui-Quan; 0000-0002-7066-246X
Gonorrhea is a disease that is spread by sexual contact, and it can potentially cause infections in the genital
region, the rectum, and even the throat. Due to the shared history between infected individuals and their
sexual partners, infected individuals will likely continue to have sexual relations with those same partners.
As a result, this article aims to investigate how memory affects the transmission of gonorrhea in a structured
population using the Caputo fractional derivative and sensitivity analysis. The model is shown to be positively
invariant with a unique bound. The existence and uniqueness criteria of the fractional model are established
using fixed-point theory. The stable nature of the model is obtained using the Ulam Hyers and Ulam Hyers
Rassias ideas. To highlight the stability of the fractional model, the stability of solution trajectories to the
disease-free and endemic steady states is graphically illustrated for the gonorrhea basic reproduction number,
𝜚∗0 < 1 and 𝜚∗0 > 1, respectively. We showed the sensitivities linked to the proposed model using the Latin
hypercube sampling, singular value analysis, box plots, scatter plots, contour plots, three-dimensional plots,
and sensitivity heat maps. We noticed that the transmission rate from females to males, 𝛽𝑓𝑚, is the most
influential parameter in the spread of the disease. From the sensitivity heat maps, it is noticed that using the
first four principal components analysis, the most sensitive state variables to the parameters in the model are
symptomatic females, recovered males, susceptible females, and recovered females. In conjunction with the
modified Adams–Bashforth method, the numerical trajectories of the fractional Caputo model are investigated.
Finally, we noticed that memory changes impact the number of incubative females and incubative males.
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Examining Dynamics of Emerging Nipah Viral Infection with Direct and Indirect Transmission Patterns: A Simulation-Based Analysis via Fractional and Fractal-Fractional Derivatives
(Hindawi, 2023-10) Ullah, Saif; Li, Shuo; AlQahtani, Salman A.; Asamoah, Joshua Kiddy K.; 0000-0002-7066-246X
(contaminated foods-to-human) transmission routes via the Caputo fractional and fractional-fractal modeling approaches. +e
model is vigorously analyzed both theoretically and numerically. +e possible equilibrium points of the system and their existence
are investigated based on the reproduction number. +e model exhibits three equilibrium points, namely, infection-free, infected
6ying foxes free, and endemic. Furthermore, novel numerical schemes are derived for the models in fractional and fractalfractional
cases. Finally, an extensive simulation is conducted to validate the theoretical results and provide an impact of the model
on the disease incidence. We believe that this study will help to incorporate such mathematical techniques to examine the complex
dynamics and control the spread of such infectious diseases.
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A fractal–fractional order model for exploring the dynamics of Monkeypox disease
(Elsevier, 2023-08) Wireko, Fredrick Asenso; Adu, Isaac Kwasi; Sebil, Charles; Asamoah, Joshua Kiddy K.; 0000-0002-7066-246X
This study explores the biological behaviour of the Monkeypox disease using a fractal–fractional operator. We
discuss the existence and uniqueness of the solution of the model using the fixed-point concept. We further
show that the Monkeypox fractal–fractional model is stable through the Hyers–Ulam and Hyers–Ulam Rassias
stability criteria. The epidemiological threshold of the model is obtained. The numerical simulation for the
proposed model is obtained using the Newton polynomial. For instance, the disease dies out at lower fractional
values. We investigated the effects of some key parameters on the dynamics of the disease. The variation
of the parameters shows that quarantine and isolation are effective approaches to managing, controlling, or
eradicating the Monkeypox disease.
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On the fractal-fractional Mittag-Leffler model of a COVID-19 and Zika Co-infection
(Elsevier, 2023-11) Rezapour, Shahram; Asamoah, Joshua Kiddy K.; Etemad, Sina; Akgül, Ali; Avcı, İbrahim; Din, Sayed M. El; 0000-0002-7066-246X
The World Health Organization declared COVID-19 a global pandemic in March 2020, which had a significant
impact on global health and economies. There have been several Zika outbreaks in different regions such as
Africa, Southeast Asia, and the Americas. Therefore, it is essential to study the dynamics of these two diseases,
taking into account their memory and recurrence effects. A new fractal-fractional hybrid Mittag-Leffler model
of COVID-19 and Zika co-dynamics is designed and studied to evaluate the effects of COVID-19 on Zika and
vice-versa. The stability analysis of the local asymptotic type at disease-free equilibrium is conducted for the
hybrid model. The existence of unique solutions to the model is established via some fixed point results.
The fractal-fractional model is proved to be Hyers–Ulam stable. With the help of Newton polynomials, we
obtain some numerical algorithms to approximate the solutions of the fractal-fractional hybrid Mittag-Leffler
model graphically. The impact of fractional and fractal orders on the dynamics of each of the epidemiological
classes is also assessed. In addition, empirical evidence from numerical simulations suggests that implementing
measures to contain the transmission of the SARS-CoV-2 virus can significantly contribute to the reduction of
co-infections involving the Zika virus. Therefore, it is imperative for healthcare systems to maintain a state of
constant vigilance in order to detect any atypical patterns or probable occurrences of co-infections, particularly
in areas where both diseases are widespread. Additionally, it is vital to consult the most recent directives
provided by health authorities, as our comprehension of diseases may undergo advancements over the course
of time.
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A mathematical model of corruption dynamics endowed with fractal–fractional derivative
(Elsevier, 2023-08) Nwajeri, Ugochukwu Kizito; Asamoah, Joshua Kiddy K.; Ugochukwu, Ndubuisi Rich; Omamea, Andrew; Jin, Zhen; 0000-0002-7066-246X
Numerous organisations across the globe have significant challenges about corruption, characterised by a
systematic, endemic, and pervasive nature that permeates various societal establishments. Hence, we propose
the fractional order model of corruption, which encompasses the involvement of corrupt individuals across
various stages of education and employment. Specifically, we examine the presence of corruption among
children in elementary schools, youths in tertiary institutions, adults in civil services, adults in government
and public offices, and individuals who have renounced their involvement in corrupt practices. The basic
reproduction number of the system was determined by utilising the next-generation matrix. The strength
number was obtained by calculating the second derivative of the corruption-related compartments. The
examined model solution’s existence, uniqueness, and stability were established using the Krasnoselski fixed
point theorem, the Banach contraction principle, and the Ulam–Hyers theorem, respectively. Based on the
numerous figures presented, our simulations indicate a positive correlation between the decline in fractal–
fractional order and the increase in the number of individuals susceptible to corruption. This phenomenon
results in an increase in the prevalence of corruption among designated sectors of the general population. The
persistence of corruption in society is a significant challenge to its eradication, as individuals who see personal
gains from engaging in corrupt practices tend to exhibit a recurring inclination towards such behaviour.
Nevertheless, it is recommended that to mitigate corruption within various corruption-prone subcategories,
there is a need to enhance the level of consciousness and promotion of anti-corruption measures throughout
all societal establishments.
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Optimal strategies for control of cholera in the presence of hyper-infective individuals
(Elsevier, 2023-09) Seidu, Baba; Wiah, Eric N.; Asamoah, Joshua Kiddy K.; 0000-0002-7066-246X
primary site of infection being the small intestine. The disease typically spreads through contaminated water
and food and becomes more pronounced in areas with poor sanitation and inadequate access to clean drinking
water. Cholera infection can lead to severe diarrhoea, dehydration, and death if left untreated. Individuals with
low personal hygiene have higher chances of spreading and/or contracting the disease. This study aims to
propound a non-linear deterministic model to study the dynamics of cholera in the presence of two groups of
individuals based on their level of personal hygiene. We categorize these individuals into low-risk and high-risk
to describe individuals with good personal hygiene and those with very low personal hygiene, respectively. The
model is shown to have two mutually exclusive fixed points, namely, the cholera-free and the cholera-persistent
equilibria, indicating the presence of forward bifurcation. It is shown that restriction of the basic reproduction
number below unity guarantees local asymptotic stability of the cholera-free fixed point. The immigration rate,
rate of disinfection, bacteria ingestion rate, and bacterial shedding rate are parameters with a higher impact
on cholera spread. Optimal control analysis is also used to determine the most cost-effective combination of
infection control, adherence to sanitation protocols, treatment control, and bacterial-shedding controls needed
to control the spread of cholera.