Mathematical Modelling of In-Vivo Dynamics of HIV Subject to the Influence of the CD8+ T-Cells

There have been many mathematical models aimed at analysing the in-vivo dynamics of HIV. However, in most cases the attention has been on the interaction between the HIV virions and the CD4+ T-cells. This paper brings in the intervention of the CD8+ T-cells in seeking, destroying, and killing the infected CD4+ T-cells during early stages of infection. The paper presents and analyses a five-component in-vivo model and applies the results in investigating the in-vivo dynamics of HIV in presence of the CD8+ T-cells. We prove the positivity and the boundedness of the model solutions. In addition, we show that the solutions are biologically meaningful. Both the endemic and virions- free equilibria are determined and their stability investigated. In addition, the basic reproductive number is derived by the next generation matrix method. We prove that the virions-free equilibrium state is locally asymptotically stable if and only if R0 < 1 and unstable otherwise. The results show that at acute infection the CD8+ T-cells play a paramount role in reducing HIV viral replication. We also observe that the model exhibits backward and trans-critical bifurcation for some set of parameters for R0 . This is a clear indication that having R0 is not sufficient condition for virions depletion.

Comparative Assessment of Zero-Inflated Models with Application to HIV Exposed Infants Data

In a typical Kenyan HIV clinical setting, there is a likelihood of registering many zeros during the routine monthly data collection of new HIV infections among HIV exposed infants (HEI). This is attributed to the implementation of the prevention of mother to child transmission (PMTCT) policies. However, even though the PMTCT policy is implemented uniformly across all public health facilities, implementation naturally differs from every facility due to differential health systems and infrastructure. This leads to structured zero among reported positive HEI (where PMTCT implementation is optimum) and non-structured zero among reported positive HEI (where PMTCT implementation is not optimum). Hence the classical zero-inflated and hurdle models that do not account for the abundance of structured and non-structured zeros in the data can give misleading results. The purpose of this study is to systematically compare performance of the various zero-inflated models with an application to HIV Exposed Infants (HEI) in the context of structured and unstructured zeros. We revisit zero-inflated, hurdle models, Poisson and negative binomial count models and conduct the simulations by varying sample size and levels of abundance zeros. Results from simulation study and real data analysis of exposed infant diagnosis show the negative binomial emerging as the best performing model when fitting data with both structured and non-structured zeros under various settings.

Assessing Efficient Risk Ratios: An Application to Surgical Stage Prediction in Cervical Cancer

Background:?Cervical cancer remains the second most commonly diagnosed cancer and the third leading cause of cancer death in developing countries. Improving clinicians’ knowledge and understanding of surgical staging is critical?in the fight against the disease. However, a systematic evaluation of different ordinal regression models based on diverse predicted outcomes has not been given its due share in literature.?Objective:?To systematically assess the flexibility of odds ratios for three popular ordinal regression models i.e.?the Multinomial Logistic (ML) model, the Continuation Ratio (CR) model and Adjacent Category Logistic (ACL) model when applying cervical cancer data in surgical stage prediction.?Method:?We systematically, compared the performance of CR, ML and the ACL as the predictive mechanisms, and evaluate the most appropriate model in the cervical cancer setting. The study considered women who visited the Oncology department at the Moi Teaching and Referral Hospital’s Chandaria Cancer and Chronic Diseases Center and were diagnosed and surgically treated for cervical cancer from January 2014?to December 2018.?Results and Conclusion:?We presented the comparison between?3?different regression models for ordinal data within the cervical cancer setting. We found that the CR model without proportional odds yielded better results?comparing Akaike Information Criterion (AIC), log likelihood ratio and residual deviance. In addition, the key prognostic factor associated with invasive cervical cancer was the (International Federation of Gynecology and Obstetrics) FIGO clinical stage which in particular, had a higher influence on the surgical Stage 2 outcomes compared to the lesser surgical stage categories. All the 5?independent features selected for classifying the patients into surgical stages were the FIGO clinical stage and partly, the presence or absence of?symptomatic vaginal discharge.

Statistical Modeling of Malaria Incidences in Apac District, Uganda

Malaria is a major cause of morbidity and mortality in Apac district, Northern Uganda. Hence, the study aimed to model malaria incidences with respect to climate variables for the period 2007 to 2016 in Apac district. Data on monthly malaria incidence in Apac district for the period January 2007 to December 2016 was obtained from the Ministry of health, Uganda whereas climate data was obtained from Uganda National Meteorological Authority. Generalized linear models, Poisson and negative binomial regression models were employed to analyze the data. These models were used to fit monthly malaria incidences as a function of monthly rainfall and average temperature. Negative binomial model provided a better fit as compared to the Poisson regression model as indicated by the residual plots and residual deviances. The Pearson correlation test indicated a strong positive association between rainfall and malaria incidences. High malaria incidences were observed in the months of August, September and November. This study showed a significant association between monthly malaria incidence and climate variables that is rainfall and temperature. This study provided useful information for predicting malaria incidence and developing the future warning system. This is an important tool for policy makers to put in place effective control measures for malaria early enough.

Estimating a Finite Population Mean under Random Non-Response in Two Stage Cluster Sampling with Replacement

Non-response is a regular occurrence in Sample Surveys. Developing estimators when non-response exists may result in large biases when estimating population parameters. In this paper, a finite population mean is estimated when non-response exists randomly under two stage cluster sampling with replacement. It is assumed that non-response arises in the survey variable in the second stage of cluster sampling. Weighting method of compensating for non-response is applied. Asymptotic properties of the proposed estimator of the population mean are derived. Under mild assumptions, the estimator is shown to be asymptotically consistent.

Using Statistical Learning to Treat Missing Data: A Case of HIV/TB Co-Infection in Kenya

In this study, we investigate the effects of missing data when estimating HIV/TB co-infection. We revisit the concept of missing data and examine three available approaches for dealing with missingness. The main objective is to identify the best method for correcting missing data in TB/HIV Co-infection setting. We employ both empirical data analysis and extensive simulation study to examine the effects of missing data, the accuracy, sensitivity, specificity and train and test error for different approaches. The novelty of this work hinges on the use of modern statistical learning algorithm when treating missingness. In the empirical analysis, both HIV data and TB-HIV co-infection data imputations were performed, and the missing values were imputed using different approaches. In the simulation study, sets of 0% (Complete case), 10%, 30%, 50% and 80% of the data were drawn randomly and replaced with missing values. Results show complete cases only had a co-infection rate (95% Confidence Interval band) of 29% (25%, 33%), weighted method 27% (23%, 31%), likelihood-based approach 26% (24%, 28%) and multiple imputation approach 21% (20%, 22%). In conclusion, MI remains the best approach for dealing with missing data and failure to apply it, results to overestimation of HIV/TB co-infection rate by 8%.

Parallelization and Acceleration of Dynamic Option Pricing Models on GPU-CPU Heterogeneous Systems

In this paper,stochastic global optimization algorithms,specifically,genetic algorithm and simulated annealing are used for the problem of calibrating the dynamic option pricing model under stochastic volatility to market prices by adopting a hybrid programming approach.The performance of this dynamic option pricing model under the obtained optimal parameters is also discussed.To enhance the model throughput and reduce latency,a heterogeneous hybrid programming approach on GPU was adopted which emphasized a data-parallel implementation of the dynamic option pricing model on a GPU-based system.Kernel offloading to the GPU of the compute-intensive segments of the pricing algorithms was done in OpenCL.The GPU approach was found to significantly reduce latency by an optimum of 541 times faster than a parallel implementation approach on the CPU,reducing the computation time from 46.24 minutes to 5.12 seconds.

A mathematical modelling study of HIV infection in two heterosexual age groups in Kenya

The control of HIV demands different interventions for different age groups.In the present manuscript,we formulate and analyze a mathematical compartmental models of HIV transmission within and between two age groups in Kenya.We fitted the model to data using MCMC technique and inferred the parameters.We also estimate the reproduction numbers,namely within age group transmission and between age groups transmission basic reproduction numbers.The analysis of the data revealed that there is significant difference in mean number of new HIV infections between males and females within the two age groups.More,particularly,females are highly infected with HIV as compared to their male counterparts.Calculation of the reproduction numbers within and between age groups provides insights into control that cannot be deduced simply from observations on the prevalence of infection.More specifically,the analysis showed that the per capita rate of HIV transmission was highest when there is interaction between young adults to adults and most HIV infections occurred in adult population.Furthermore,the sensitivity analysis demonstrated that the reproduction numbers depend mainly on the probabilities of infection.This results can be used to guide HIV interventions,condom distribution and antiretroviral therapy.Precisely,the results can be used to educate the young adults on practicing safe sex with their partners in order to contain the occurrence of new infections.

Age-structured model for COVID-19: Effectiveness of social distancing and contact reduction in Kenya

Coronavirus disease 2019 is caused by severe acute respiratory syndrome coronavirus 2.Kenya reported its first case on March 13,2020 and by March 16,2020 she instituted physical distancing strategies to reduce transmission and flatten the epidemic curve.An age-structured compartmental model was developed to assess the impact of the strategies on COVID-19 severity and burden.Contacts between different ages are incorporated via contact matrices.Simulation results show that 45%reduction in contacts for 60-days period resulted to 11.5e13%reduction of infections severity and deaths,while for the 190-days period yielded 18.8e22.7%reduction.The peak of infections in the 60-days mitigation was higher and happened about 2 months after the relaxation of mitigation as compared to that of the 190-days mitigation,which happened a month after mitigations were relaxed.Low numbers of cases in children under 15 years was attributed to high number of asymptomatic cases.High numbers of cases are reported in the 15e29 years and 30e59 years age bands.Two mitigation periods,considered in the study,resulted to reductions in severe and critical cases,attack rates,hospital and ICU bed demands,as well as deaths,with the 190-days period giving higher reductions.

FAIR Equivalency, Regulatory Framework and Adoption Potential of FAIR Guidelines in Health in Kenya

This study explored the regulatory framework in Kenya that may facilitate the implementation of the FAIR Guidelines in health research, as well as the possibility of adopting the FAIR Guidelines at the national level. Fourteen key documents pivotal to the emerging digital health sector in Kenya were identified and analysed using a comprehensive coding and labelling approach based on a binary system for whether or not they mention the FAIR Guidelines or terms and vocabulary related to the FAIR Guidelines. The analysis revealed gaps in data stewardship that could be filled by the implementation of the FAIR Guidelines and, although the documents analysed do not explicitly mention the FAIR Guidelines, FAIR Equivalent terminology and practices are mentioned in varying detail. However, our analysis shows that there are still no provisions for the introduction and implementation of the FAIR Guidelines in health research in Kenya. Therefore, we recommend that the leadership be provided with a comprehensive introduction to the FAIR Guidelines, success stories about the FAIRification of data and research infrastructure in other parts of the world, and a demonstration of the steps needed for the FAIRification of health data in Kenya.

SARS-COV-2 outbreak and control in Kenya - Mathematical model analysis

The coronavirus disease 2019(COVID-19)pandemic reached Kenya in March 2020 with the initial cases reported in the capital city Nairobi and in the coastal area Mombasa.As reported by the World Health Organization,the outbreak of COVID-19 has spread across the world,killed many,collapsed economies and changed the way people live since it was first reported inWuhan,China,in the end of 2019.As at the end of December 2020,it had led to over 2.8 million confirmed cases in Africa with over 67 thousand deaths.The trend poses a huge threat to global public health.Understanding the early transmission dynamics of the infection and evaluating the effectiveness of control measures is crucial for assessing the potential for sustained transmission to occur in new areas.We employed a SEIHCRD mathematical transmission model with reported Kenyan data on cases of COVID-19 to estimate how transmission varies over time.The model is concise in structure,and successfully captures the course of the COVID-19 outbreak,and thus sheds light on understanding the trends of the outbreak.The next generation matrix approach was adopted to calculate the basic reproduction number(R_(0))from the model to assess the factors driving the infection.The model illustrates the effect of mass testing on COVID-19 as well as individual self initiated behavioral change.The results have significant impact on the management of COVID-19 and implementation of prevention policies.The results from the model analysis shows that aggressive and effective mass testing as well as individual self initiated behaviour change play a big role in getting rid of the COVID-19 epidemic otherwise the rate of infection will continue to increase despite the increased rate of recovery.

Optimal control analysis of hepatocytic-erythrocytic dynamics of Plasmodium falciparum malaria

This paper presents an in-host malaria model subject to anti-malarial drug treatment and malaria vaccine antigens combinations.Pontryagin's Maximum Principle is applied to establish optimal control strategies against infected erythrocytes,infected hepatocytes and malaria parasites.Results from numerical simulation reveal that a combination of preerythrocytic vaccine antigen,blood schizontocide and gametocytocide drugs would offer the best strategy to eradicate clinical P.falciparum malaria.Sensitivity analysis,further reveal that the efficacy of blood schizontocides and blood stage vaccines are crucial in the control of clinical malaria infection.Futhermore,we found that an effective blood schizontocide should be used alongside efficacious blood stage vaccine for rapid eradication of infective malaria parasites.The authors hope that the results of this study will help accelerate malaria elimination efforts by combining malaria vaccines and anti-malarial drugs against the deadly P.falciparum malaria.

Forecasting the spread of the COVID-19 pandemic in Kenya using SEIR and ARIMA models

COVID-19,a coronavirus disease 2019,is an ongoing pandemic caused by severe acute respiratory syndrome coronavirus 2(SARS-CoV-2).The first case in Kenya was identified on March 13,2020,with the pandemic increasing to about 237,000 confirmed cases and 4,746 deaths by August 2021.We developed an SEIR model forecasting the COVID-19 pandemic in Kenya using an Autoregressive Integrated moving averages(ARIMA)model.The average time difference between the peaks of wave 1 to wave 4 was observed to be about 130 days.The 4th wave was observed to have had the least number of daily cases at the peak.According to the forecasts made for the next 60 days,the pandemic is expected to continue for a while.The 4th wave peaked on August 26,2021(498th day).By October 26,2021(60th day),the average number of daily infections will be 454 new cases and 40 severe cases,which would require hospitalization,and 16 critically ill cases requiring intensive care unit services.The findings of this study are key in developing informed mitigation strategies to ensure that the pandemic is contained and inform the preparedness of policymakers and health care workers.