Browsing by Author "Paul, James"

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Mathematical Approach to Investigate Stress due to Control Measures to Curb COVID-19
(Hindawi, 2022-01-13) Paul, James; Mirau, Silas; Mbalawata, Isambi
COVID-19 is a world pandemic that has affected and continues to affect the social lives of people. Due to its social and economic impact, different countries imposed preventive measures that are aimed at reducing the transmission of the disease. Such control measures include physical distancing, quarantine, hand-washing, travel and boarder restrictions, lockdown, and the use of hand sanitizers. Quarantine, out of the aforementioned control measures, is considered to be more stressful for people to manage. When people are stressed, their body immunity becomes weak, which leads to multiplying of coronavirus within the body. Therefore, a mathematical model consisting of six compartments, Susceptible-Exposed-Quarantine-Infectious-Hospitalized-Recovered (SEQIHR) was developed, aimed at showing the impact of stress on the transmission of COVID-19 disease. From the model formulated, the positivity, bounded region, existence, uniqueness of the solution, the model existence of free and endemic equilibrium points, and local and global stability were theoretically proved. The basic reproduction number () was derived by using the next-generation matrix method, which shows that, when , the disease-free equilibrium is globally asymptotically stable whereas when the endemic equilibrium is globally asymptotically stable. Moreover, the Partial Rank Correlation Coefficient (PRCC) method was used to study the correlation between model parameters and . Numerically, the SEQIHR model was solved by using the Rung-Kutta fourth-order method, while the least square method was used for parameter identifiability. Furthermore, graphical presentation revealed that when the mental health of an individual is good, the body immunity becomes strong and hence minimizes the infection. Conclusively, the control parameters have a significant impact in reducing the transmission of COVID-19.
Mathematical modeling of vaccination as a control measure of stress to fight COVID-19 infections
(Elsevier, 2023-01) Paul, James; Mbalawata, Isambi; Mirau, Silas; Masandawa, Lemjini
The world experienced the life-threatening COVID-19 disease worldwide since its inversion. The whole world experienced difficult moments during the COVID-19 period, whereby most individual lives were affected by the disease socially and economically. The disease caused millions of illnesses and hundreds of thousands of deaths worldwide. To fight and control the COVID-19 disease intensity, mathematical modeling was an essential tool used to determine the potentiality and seriousness of the disease. Due to the effects of the COVID-19 disease, scientists observed that vaccination was the main option to fight against the disease for the betterment of human lives and the world economy. Unvaccinated individuals are more stressed with the disease, hence their body’s immune system are affected by the disease. In this study, the 𝑆𝑉 𝐸𝐼𝐻𝑅 deterministic model of COVID- 19 with six compartments was proposed and analyzed. Analytically, the next-generation matrix method was used to determine the basic reproduction number (𝑅0). Detailed stability analysis of the no-disease equilibrium (𝐸0) of the proposed model to observe the dynamics of the system was carried out and the results showed that 𝐸0 is stable if 𝑅0 < 1 and unstable when 𝑅0 > 1. The Bayesian Markov Chain Monte Carlo (MCMC) method for the parameter identifiability was discussed. Moreover, the sensitivity analysis of 𝑅0 showed that vaccination was an essential method to control the disease. With the presence of a vaccine in our 𝑆𝑉 𝐸𝐼𝐻𝑅 model, the results showed that 𝑅0 = 0.208, which means COVID-19 is fading out of the community and hence minimizes the transmission. Moreover, in the absence of a vaccine in our model, 𝑅0 = 1.7214, which means the disease is in the community and spread very fast. The numerical simulations demonstrated the importance of the proposed model because the numerical results agree with the sensitivity results of the system. The numerical simulations also focused on preventing the disease to spread in the community
Mathematical modelling approach to investigate transmission dynamics of covid-19 with some control parameters
(NM-AIST, 2022-06) Paul, James
COVID-19 is a world pandemic that has affected and continues to affect human lives, socially and economically. Worldwide governments enforced preventive measures aimed at reducing the disease transmission due to its social and economic impact. Examples of such measures are phys ical separation, quarantine, hand-washing, travel bans and border restrictions, lockdown, and the use of hand sanitizers. Some of the control measures like quarantine was the most stressful strat egy for people to manage. To examine the impact of stress on the transmission of COVID-19, this dissertation developed a mathematical model with six compartments; Susceptible-Exposed Quarantine-Infectious-Hospitalized-Recovered (SEQIHR). The model was then analyzed both theoretically and numerically. In theoretical analysis, terms like positivity, bounded region, exis tence, uniqueness of the solution, model existence of free and endemic equilibrium points, local and global stability are all utilized. The basic reproduction number (R0) was calculated using the next-generation matrix approach. When R0 < 1, the disease-free equilibrium is globally asymp totically stable, whereas when R0 > 1, the endemic equilibrium is globally asymptotically stable. The Partial Rank Correlation Coefficient (PRCC) was used to evaluate the relationship between model parameters and R0. The model was numerically solved using the fourth-order Runge-Kutta method, and parameter identifiability was achieved using least square and Markov Chain Monte Carlo (MCMC) methods. The formulated deterministic model explored the impact of stress in quarantine to the human population and revealed that when an individual’s mental health is good, the body immunity becomes strong. Conclusively, the control parameters have a considerable impact on COVID-19 transmission minimization.
Modeling nosocomial infection of COVID-19 transmission dynamics
(Elsevier, 2022-06) Masandawa, Lemjini; Mirau, Silas; Mbalawata, Isambi; Paul, James; Kreppel, Katharina; Msamba, Oscar
COVID-19 epidemic has posed an unprecedented threat to global public health. The disease has alarmed the healthcare system with the harm of nosocomial infection. Nosocomial spread of COVID-19 has been discovered and reported globally in different healthcare facilities. Asymptomatic patients and super-spreaders are sough to be among of the source of these infections. Thus, this study contributes to the subject by formulating a 𝑆𝐸𝐼𝐻𝑅 mathematical model to gain the insight into nosocomial infection for COVID-19 transmission dynamics. The role of personal protective equipment 𝜃 is studied in the proposed model. Benefiting the next generation matrix method, 𝑅0 was computed. Routh–Hurwitz criterion and stable Metzler matrix theory revealed that COVID-19-free equilibrium point is locally and globally asymptotically stable whenever 𝑅0 < 1. Lyapunov function depicted that the endemic equilibrium point is globally asymptotically stable when 𝑅0 > 1. Further, the dynamics behavior of 𝑅0 was explored when varying 𝜃. In the absence of 𝜃, the value of 𝑅0 was 8.4584 which implies the expansion of the disease. When 𝜃 is introduced in the model, 𝑅0 was 0.4229, indicating the decrease of the disease in the community. Numerical solutions were simulated by using Runge–Kutta fourth order method. Global sensitivity analysis is performed to present the most significant parameter. The numerical results illustrated mathematically that personal protective equipment can minimizes nosocomial infections of COVID-19.