Stability and global sensitivity analysis of the transmission dynamics of malaria with relapse and ignorant infected humans

In this paper we present a more realistic mathematical model for the transmission dynamics of malaria by extending the classical SEIRS scheme and the model of Hai-Feng Huo and Guang-Ming Qiu [21] by adding the ignorant infected humans compartment. We analyze the global asymptotically stabilities of the model by the use of the basic reproduction number R_0 and we prove that when R_0≦1, the disease-free equilibrium is globally asymptotically stable. That is malaria dies out in the population. When R_0>1, there exists a co-existing unique endemic equilibrium which is globally asymptotically stable. The global sensitivity analysis have been done through the partial rank correlation coefficient using the samples generated by the use of latin hypercube sampling method and shows that the most influence parameters in the spread of malaria are the proportion θ of infectious humans who recover and the recovery rate γ of infectious humans. In order to eradicate malaria, we have to decrease the number of ignorant infected humans by testing peoples and treat them. Numerical simulations show that malaria can be also controlled or eradicated by increasing the recovery rate γ of infectious humans, decreasing the number of ignorant infected humans and decreasing the average number n of mosquito bites.

A mathematical model of the dynamics of lymphatic filariasis in Caraga Region, the Philippines

Despite being one of the first countries to implement mass drug administration (MDA) for elimination of lymphatic filariasis (LF) in 2001 after a pilot study in 2000, the Philippines is yet to eliminate the disease as a public health problem with 6 out of the 46 endemic provinces still implementing MDA for LF as of 2018. In this work, we propose a mathematical model of the transmission dynamics of LF in the Philippines and a control strategy for its elimination using MDA. Sensitivity analysis using the Latin hypercube sampling and partial rank correlation coefficient methods suggests that the infected human population is most sensitive to the treatment parameters. Using the available LF data in Caraga Region from the Philippine Department of Health, we estimate the treatment rates r 1 and r 2 using the least-squares parameter estimation technique. Parameter bootstrapping showed small variability in the parameter estimates. Finally, we apply optimal control theory with the objective of minimizing the infected human population and the corresponding implementation cost of MDA, using the treatment coverage γ as the control parameter. Simulation results highlight the importance of maintaining a high MDA coverage per year to effectively minimize the infected population by the year 2030.

Quantifying the dose-dependent impact of intracellular amyloid beta in a mathematical model of calcium regulation in xenopus oocyte

Alzheimer’s disease (AD) is a devastating illness affecting over 40 million people worldwide. Intraneuronal rise of amyloid beta in its oligomeric forms (iAβOs), has been linked to the pathogenesis of AD by disrupting cytosolic Ca2+ homeostasis. However, the specific mechanisms of action are still under debate and intense effort is ongoing to improve our understanding of the crucial steps involved in the mechanisms of AβOs toxicity. We report the development of a mathematical model describing a proposed mechanism by which stimulation of Phospholipase C (PLC) by iAβO, triggers production of IP3 with consequent abnormal release of Ca2+ from the endoplasmic reticulum (ER) through activation of IP3 receptor (IP3R) Ca2+ channels. After validating the model using experimental data, we quantify the effects of intracellular rise in iAβOs on model solutions. Our model validates a dose-dependent influence of iAβOs on IP3-mediated Ca2+ signaling. We investigate Ca2+ signaling patterns for small and large iAβOs doses and study the role of various parameters on Ca2+ signals. Uncertainty quantification and partial rank correlation coefficients are used to better understand how the model behaves under various parameter regimes. Our model predicts that iAβO alter IP3R sensitivity to IP3 for large doses. Our analysis also shows that the upstream production of IP3 can influence Aβ-driven solution patterns in a dose-dependent manner. Model results illustrate and confirm the detrimental impact of iAβOs on IP3 signaling.

Availability Analysis of Hybrid Systems Consisting of Main Units and Cold Standby Processors

The present paper studies availability of four hybrid systems configured as series-parallel systems. Each system or configuration consisting of main units and their corresponding processors. Configuration I consist of three processors is a 2-out-of-3 unit connected to 2-out-of-3 processors, Configuration II is a 2-out-of-3 unit connected to 2-out-of-4 processors, Configuration III is a 2-out-of-4 unit connected to 2-out-of-4 processors while Configuration IV is a 2-out-of-4 unit connected to 2-out-of-3 processors. The failure and repair times of units and their processors are assumed to be exponentially distributed. Explicit expressions for steady state availability are developed for each system using first order linear differential difference equations and validated by performing numerical experiments. Analysis of the effect of various system parameters on availability was performed. Graphical illustrations are given to highlight important results. The systems are ranked based on their availability and found that Configuration IV is better. Sensitivity analysis on the model’s outcomes are performed using partial rank correlation coefficients (PRCC) to determine the most critical parameters leading to increase (decrease) in the value of availability.

Modeling and Control of the Public Opinion: An Agree-Disagree Opinion Model

In this paper, we aim to investigate optimal control to a new mathematical model that describes agree-disagree opinions during polls, which we presented and analyzed in Bidah et al., 2020. We first present the model and recall its different compartments. We formulate the optimal control problem by supplementing our model with a objective functional. Optimal control strategies are proposed to reduce the number of disagreeing people and the cost of interventions. We prove the existence of solutions to the control problem, we employ Pontryagin’s maximum principle to find the necessary conditions for the existence of the optimal controls, and Runge–Kutta forward-backward sweep numerical approximation method is used to solve the optimal control system, and we perform numerical simulations using various initial conditions and parameters to investigate several scenarios. Finally, a global sensitivity analysis is carried out based on the partial rank correlation coefficient method and the Latin hypercube sampling to study the influence of various parameters on the objective functional and to identify the most influential parameters.

Prevention and Control of Tuberculosis Relying on a Tuberculosis Dynamic Model Based on the Cases of American

Background: Tuberculosis (TB) which is a preventable and curable disease, is claimed as the second largest number of fatalities and there are 9,025 cases reported in the United State in 2018. Many researches have done a lot of research and achieved remarkable results, but TB is also a serious problem for human being.The study is a further exploration. Methods: In the paper, we propose a new dynamic model to study the transmission dynamics of TB, then use global differential evolution and local sequential quadratic programming (DESQP) optimization algorithm to estimate parameters of the model. Finally, we use Latin hypercube sampling (LHS) and partial rank correlation coefficients (PRCC) to analyze the influence of parameters on the basic reproduction number (R0) and the total infectious (including the diagnosed, undiagnosed and incomplete treatment infectious), respectively. Results: By the research, the basic reproduction is computed as 2.3597 which means TB will be epidemic in US. The diagnosed rate is 0.6082 which means the undiagnosed will be diagnosed after 1.6442 years. The diagnosed will be recovered with an average of 1.9912 years, especially, some diagnosed will end the treatment after 1.7550 years, for some reasons. By the study, it’s shown that there are 2.4% of the recovered will be reactivated and 13.88% of the newborn will be vaccination. However, the immunity will be lose after about 19.6078 years. Conclusion: Through the results of this study, we give some suggestions to help prevent and control the TB epidemic in the United State, such as prolonging the protection period of the vaccine by developing new and more effective vaccines to prevent TB, using the chemoprophylaxis for incubation patients to prevent their conversion into active TB; raising people’s awareness of prevention and control of TB and treatment after illness; isolation treatment for the infected to reduce the spread of TB. According to the latest report, in the announcement came at the first WHO Global Ministerial Conference on Ending Tuberculosis in the Sustainable Development Era, we predict that it’s difficult to control TB in 2030.

Mathematical Modeling to Estimate the Reproductive Number and the Outbreak Size of COVID-19: The case of India and the World

Coronavirus disease (COVID-19) has become a global pandemic with more than 218,000 deaths in 211 different countries around the world. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the virus responsible for this deadliest disease. This paper describes a mathematical model for India, a country with the second highest population in the world with an extremely high population density of about 464 people per km2. This disease has multiphasic actions and reaction mode and our model SEIAQIm is based on six compartmental groups in the form of susceptible, exposed, infectious, asymptomatic, quarantine, and recovered immune factions. Latin Hypercube Sampling Partial Rank Correlation Coefficient method was used for the data analysis and model fitting. According to our model, India would reach its basic reproduction number R0=0.97 on May 14, 2020 with a total number of 73,800 estimated cases. Further, this study also equates the world's situation using the same model system and predicts by May 7, 2020 with a total number of 3,772,000 estimated confirmed cases. Moreover, the current mathematical model highlights the importance of social distancing as an effective method of containing spread of COVID-19.

Modelling the transmission dynamics of COVID-19 in six high burden countries

The new coronavirus disease, officially known as COVID-19, originated in China in 2019 and has since spread around the globe. We presented a modified Susceptible-Latent-Infected-Removed (SLIR) compartmental model of COVID-19 disease transmission with nonlinear incidence during the epidemic period. We provided the model calibration to estimate parameters with day wise corona virus (COVID-19) data i.e. reported cases by worldometer from the period of 15th February to 30th March, 2020 in six high burden countries including Australia, Italy, Spain, USA, UK and Canada. We estimate transmission rates for each countries and found that the highest transmission rate country in Spain, which may be increase the new cases and deaths in Spain than the other countries. Sensitivity analysis was used to identify the most important parameters through the partial rank correlation coefficient method. We found that the transmission rate of COVID-19 had the largest influence on the prevalence. We also provides the prediction of new cases in COVID-19 until May 18, 2020 using the developed model and recommends, control strategies of COVID-19. The information that we generated from this study would be useful to the decision makers of various organizations across the world including the Ministry of Health in Australia, Italy, Spain, USA, UK and Canada to control COVID-19.

Stability and Global Sensitivity Analysis for an Agree-Disagree Model: Partial Rank Correlation Coefficient and Latin Hypercube Sampling Methods

In this paper, we present a new mathematical model that describes agree-disagree opinions during polls. We first present the model and its different compartments. Then, we use the next-generation matrix method to compute thresholds of equilibrium stability. We perform the stability analysis of equilibria to determine under which conditions these equilibrium points are stable or unstable. We show that the existence and stability of these equilibria are controlled by the calculated thresholds. Finally, we also perform several computational and statistical experiments to validate the theoretical results obtained in this work. To study the influence of various parameters on these thresholds and to identify the most influential parameters, a global sensitivity analysis is carried out based on the partial rank correlation coefficient method and the Latin hypercube sampling.