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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.