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

2021 ◽  
Vol 8 (6) ◽  
pp. 201965
Author(s):  
Pamela Kim N. Salonga ◽  
Victoria May P. Mendoza ◽  
Renier G. Mendoza ◽  
Vicente Y. Belizario

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.

2020 ◽  
Author(s):  
Durgesh Nandini Sinha

Abstract 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.


PLoS ONE ◽  
2021 ◽  
Vol 16 (1) ◽  
pp. e0246116
Author(s):  
Joseph Minicucci ◽  
Molly Alfond ◽  
Angelo Demuro ◽  
David Gerberry ◽  
Joe Latulippe

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.


2022 ◽  
Author(s):  
Yves Tinda Mangongo ◽  
Joseph-Désiré Kyemba Bukweli ◽  
Justin Dupar Busili Kampempe ◽  
Rostin Matendo Mabela ◽  
Justin Manango Wazute Munganga

Abstract 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.


2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Sara Bidah ◽  
Omar Zakary ◽  
Mostafa Rachik

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.


2018 ◽  
Vol 26 (04) ◽  
pp. 603-632 ◽  
Author(s):  
PANKAJ KUMAR TIWARI ◽  
IULIA MARTINA BULAI ◽  
FRANCESCA BONA ◽  
EZIO VENTURINO ◽  
ARVIND KUMAR MISRA

In this paper, we introduce a model to study the effects of human populations on fish survival in aquatic media. Directly, this occurs by fishing. Indirectly instead this is related to other human actions that lead to organic pollution and consequently low dissolved oxygen(DO) levels, thereby harming the aquatic fauna. Mathematically, we consider various nonlinear processes involving human population, organic pollutants, bacteria, DO and fish population. In the present study, our aim is to investigate the effect of depleted level of DO on the survival of fish populations in such an aquatic system. The case study in consideration is represented by the Ulsoor lake, Bengaluru, India. Into it, huge amounts of sewage were discharged and resulted in reduction of DO level and massive fish mortality. Equilibria are analyzed for feasibility and stability, substantiated via numerical simulations. Global sensitivity analysis identifies the important parameters having a significant impact on the fish population. The Partial Rank Correlation Coefficients (PRCCs) values of fish population in the lake with respect to input parameters of the system show that the growth rate of humans in the lake watershed has maximum negative correlation while the growth in the fish population due to DO has maximum positive correlation with the density of fish population in the lake. The results show that increase in human population may decrease fish population in the system to very low values. However, by controlling additional dissolved organic loads coming from domestic sewage, farm waste and many other sources, the level of DO can be brought back to values that allow fish survival. Maintaining it at these levels would preserve the ecosystem.


SIMULATION ◽  
2017 ◽  
Vol 93 (7) ◽  
pp. 543-552 ◽  
Author(s):  
Ojaswita Chaturvedi ◽  
Mandu Jeffrey ◽  
Edward Lungu ◽  
Shedden Masupe

Epidemic modeling can be used to gain better understanding of infectious diseases, such as diarrhea. In the presented research, a continuous mathematical model has been formulated for diarrhea caused by salmonella. This model has been analyzed and simulated to be established in a functioning form. Elementary model analysis, such as working out the disease-free state and basic reproduction number, has been done for this model. The basic reproduction number has been calculated using the next generation matrix method. Stability analysis of the model has been done using the Routh–Hurwitz method. Sensitivity analysis and parameter estimation have been completed for the system too using MATLAB packages that work on the Latin Hypercube Sampling and Partial Rank Correlation Coefficient methods. It was established that as long as R0 < 1, there will be no epidemic. Upon simulation using assumed parameter values, the results produced comprehended the epidemic theory and practical situations. The system was proven stable using the Routh–Hurwitz criterion and parameter estimation was successfully completed. Salmonella diarrhea has been successfully modeled and analyzed in this research. This model has been flexibly built and it can be integrated onto certain platforms to be used as a predictive system to prevent further infections of salmonella diarrhea.


2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
M. L. Diagne ◽  
H. Rwezaura ◽  
S. Y. Tchoumi ◽  
J. M. Tchuenche

We formulate and theoretically analyze a mathematical model of COVID-19 transmission mechanism incorporating vital dynamics of the disease and two key therapeutic measures—vaccination of susceptible individuals and recovery/treatment of infected individuals. Both the disease-free and endemic equilibrium are globally asymptotically stable when the effective reproduction number R 0 v is, respectively, less or greater than unity. The derived critical vaccination threshold is dependent on the vaccine efficacy for disease eradication whenever R 0 v > 1 , even if vaccine coverage is high. Pontryagin’s maximum principle is applied to establish the existence of the optimal control problem and to derive the necessary conditions to optimally mitigate the spread of the disease. The model is fitted with cumulative daily Senegal data, with a basic reproduction number R 0 = 1.31 at the onset of the epidemic. Simulation results suggest that despite the effectiveness of COVID-19 vaccination and treatment to mitigate the spread of COVID-19, when R 0 v > 1 , additional efforts such as nonpharmaceutical public health interventions should continue to be implemented. Using partial rank correlation coefficients and Latin hypercube sampling, sensitivity analysis is carried out to determine the relative importance of model parameters to disease transmission. Results shown graphically could help to inform the process of prioritizing public health intervention measures to be implemented and which model parameter to focus on in order to mitigate the spread of the disease. The effective contact rate b , the vaccine efficacy ε , the vaccination rate v , the fraction of exposed individuals who develop symptoms, and, respectively, the exit rates from the exposed and the asymptomatic classes σ and ϕ are the most impactful parameters.


2020 ◽  
Vol 2020 ◽  
pp. 1-14 ◽  
Author(s):  
Sara Bidah ◽  
Omar Zakary ◽  
Mostafa Rachik

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.


2020 ◽  
Vol 48 (1) ◽  
Author(s):  
Rosie K. Manolas ◽  
Mike Kama ◽  
Merelesita Rainima-Qaniuci ◽  
Vinaisi D. Bechu ◽  
Samuela Tuibeqa ◽  
...  

Abstract Background Lymphatic filariasis (LF) is a major public health problem in the Pacific Region, including in Fiji. Through transmission by the mosquito vector Aedes, Fiji has suffered the burden of remaining endemic with LF despite efforts at elimination prior to 1999. In the year 1999, Fiji agreed to take part in the Pacific Programme for Elimination of LF (PacELF) and the Global Programme to Eliminate LF. Methods This study reviewed and collated past data on LF in Fiji between 1997 and 2007. Sources included published papers as well as unpublished PacELF and WHO program meeting and survey reports. Records were held at Fiji’s Department of Health and Medical Services, James Cook University and the WHO office in Suva, Fiji. Results Baseline surveys between 1997 and 2002 showed that Fiji was highly endemic for LF with an estimated 16.6% of the population antigen positive and 6.3% microfilaria positive at that time. Five rounds of annual mass drug administration (MDA) using albendazole and diethylcarbamazine commenced in 2002. Programmatic coverage reported was 58–70% per year, but an independent coverage survey in 2006 in Northern Division after the fifth MDA suggested that actual coverage may have been higher. Monitoring of the program consisted of antigen prevalence surveys in all ages with sentinel and spot check surveys carried out in 2002 (pre MDA), 2004, and 2005, together with knowledge, attitude, and practice surveys. The stop-MDA survey (C survey) in 2007 was a nationwide stratified cluster survey of all ages according to PacELF guidelines, designed to sample by administrative division to identify areas still needing MDA. The national antigen prevalence in 2007 was reduced by more than a third to 9.5%, ranging from 0.9% in Western Division to 15.4% in Eastern Division, while microfilaria prevalence was reduced by almost four-fifths to 1.4%. Having not reached the target threshold of 1% prevalence in all ages, Fiji wisely decided to continue MDA after 2007 but to move from nationwide implementation to four (later five) separate evaluation units with independent timelines using global guidelines, building on program experience to put more emphasis on increasing coverage through prioritized communication strategies, community participation, and morbidity alleviation. Conclusion Fiji conducted nationwide MDA for LF annually between 2002 and 2006, monitored by extensive surveys of prevalence, knowledge, and coverage. From a high baseline prevalence in all divisions, large reductions in overall and age-specific prevalence were achieved, especially in the prevalence of microfilariae, but the threshold for stopping MDA was not reached. Fiji has a large rural and geographically widespread population, program management was not consistent over this period, and coverage achieved was likely not optimal in all areas. After learning from these many challenges and activities, Fiji was able to build on the progress achieved and the heterogeneity observed in prevalence to realign towards a more stratified and improved program after 2007. The information presented here will assist the country to progress towards validating elimination in subsequent years.


Author(s):  
Pierre Magal ◽  
Ousmane Seydi ◽  
Glenn Webb ◽  
Yixiang Wu

A mathematical model of the dengue epidemic in the Philippines is developed to analyse the vaccination of children in 2016–2017. Reported case data and reported mortality data from the Philippines Department of Health is used to analyze quantitatively this vaccination program. The model compares the epidemic outcomes of no vaccination of children, vaccination only of previously infected children, and vaccination of all children.


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