Modelling the Survival of Western Honey Bee Apis mellifera and the African Stingless Bee Meliponula ferruginea Using Semiparametric Marginal Proportional Hazards Mixture Cure Model

Classical survival analysis assumes all subjects will experience the event of interest, but in some cases, a portion of the population may never encounter the event. These survival methods further assume independent survival times, which is not valid for honey bees, which live in nests. The study introduces a semi-parametric marginal proportional hazards mixture cure (PHMC) model with exchangeable correlation structure, using generalized estimating equations for survival data analysis. The model was tested on clustered right-censored bees survival data with a cured fraction, where two bee species were subjected to different entomopathogens to test the effect of the entomopathogens on the survival of the bee species. The Expectation-Solution algorithm is used to estimate the parameters. The study notes a weak positive association between cure statuses (ρ1=0.0007) and survival times for uncured bees (ρ2=0.0890), emphasizing their importance. The odds of being uncured for A. mellifera is higher than the odds for species M. ferruginea. The bee species, A. mellifera are more susceptible to entomopathogens icipe 7, icipe 20, and icipe 69. The Cox-Snell residuals show that the proposed semiparametric PH model generally fits the data well as compared to model that assume independent correlation structure. Thus, the semi parametric marginal proportional hazards mixture cure is parsimonious model for correlated bees survival data.

Comparison of Semi-Parametric Shared Frailty Models for Bees’Survival

Survival analysis is a fundamental tool in medical science for time-to-event data. However, its application to colony organisms like bees poses challenges due to their social nature. Traditional survival models may not accurately capture the interdependence among individuals within a colony. Frailty models, accounting for shared risks within groups, offer a promising alternative. This study evaluates the performance of semi-parametric shared frailty models (gamma, inverse normal, and positive stable-in comparison to the traditional Cox model using bees’ survival data). We examined the effect of misspecification of the frailty distribution on regression and heterogeneity parameters using simulation and concluded that the heterogeneity parameter was more sensitive to misspecification of the frailty distribution and choice of initial parameters (cluster size and true heterogeneity parameter) compared to the regression parameter. From the data, parameter estimates for covariates were close for the four models but slightly higher for the Cox model. The shared gamma frailty model provided a better fit to the data in comparison with the other models. Therefore, when focusing on regression parameters, the gamma frailty model is recommended. This research underscores the importance of tailored survival methodologies for accurately analyzing time-to-event data in social organisms.

Inferring Multi-Type Birth-Death Parameters for a Structured Host Population with Application to HIV Epidemic in Africa

Human Immunodeficiency Virus (HIV) dynamics in Africa are purely characterised by sparse sampling of DNA sequences for individuals who are infected. There are some sub-groups that are more at risk than the general population. These sub-groups have higher infectivity rates. We came up with a likelihood inference model of multi-type birth-death process that can be used to make inference for HIV epidemic in an African setting. We employ a likelihood inference that incorporates a probability of removal from infectious pool in the model. We have simulated trees and made parameter inference on the simulated trees as well as investigating whether the model distinguishes between heterogeneous and homogeneous dynamics. The model makes fairly good parameter inference. It distinguishes between heterogeneous and homogeneous dynamics well. Parameter estimation was also performed under sparse sampling scenario. We investigated whether trees obtained from a structured population are more balanced than those from a non-structured host population using tree statistics that measure tree balance and imbalance. Trees from non-structured population were more balanced basing on Colless and Sackin indices.

Stability Analysis of a Deterministic Epidemic Model in Metapopulation Setting

We present in this article an epidemic model with saturated in metapopulation setting. We develop the mathematical modelling of HIV transmission among adults in Metapopulation setting. We discussed the positivity of the system. We calculated the reproduction number, If ?for , then each infectious individual in Sub-Population j infects on average less than one other person and the disease is likely to die out. Otherwise, if ?for , then each infectious individual in Sub-Population j infects on average more than one other person;the infection could therefore establish itself in the population and become endemic. An epidemic model, where the presence or absence of an epidemic wave is characterized by the value of ?both ideas of the inner equilibrium point of stability properties are discussed.

Predicting the Underlying Structure for Phylogenetic Trees Using Neural Networks and Logistic Regression

Understanding an underlying structure for phylogenetic trees is very important as it informs on the methods that should be employed during phylogenetic inference. The methods used under a structured population differ from those needed when a population is not structured. In this paper, we compared two supervised machine learning techniques, that is artificial neural network (ANN) and logistic regression models for prediction of an underlying structure for phylogenetic trees. We carried out parameter tuning for the models to identify optimal models. We then performed 10-fold cross-validation on the optimal models for both logistic regression?and ANN. We also performed a non-supervised technique called clustering to identify the number of clusters that could be identified from simulated phylogenetic trees. The trees were from?both structured?and non-structured populations. Clustering and prediction using classification techniques were?done using tree statistics such as Colless, Sackin and cophenetic indices, among others. Results from 10-fold cross-validation revealed that both logistic regression and ANN models had comparable results, with both models having average accuracy rates of over 0.75. Most of the clustering indices used resulted in 2 or 3 as the optimal number of clusters.

Spatio-Temporal Variation of HIV Infection in Kenya

Disease mapping is the study of the distribution of disease relative risks or rates in space and time, and normally uses generalized linear mixed models (GLMMs) which includes fixed effects and spatial, temporal, and spatio-temporal random effects. Model fitting and statistical inference are commonly accomplished through the empirical Bayes (EB) and fully Bayes (FB) approaches. The EB approach usually relies on the penalized quasi-likelihood (PQL), while the FB approach, which has increasingly become more popular in the recent past, usually uses Markov chain Monte Carlo (McMC) techniques. However, there are many challenges in conventional use of posterior sampling via McMC for inference. This includes the need to evaluate convergence of posterior samples, which often requires extensive simulation and can be very time consuming. Spatio-temporal models used in disease mapping are often very complex and McMC methods may lead to large Monte Carlo errors if the dimension of the data at hand is large. To address these challenges, a new strategy based on integrated nested Laplace approximations (INLA) has recently been recently developed as a promising alternative to the McMC. This technique is now becoming more popular in disease mapping because of its ability to fit fairly complex space-time models much more quickly than the McMC. In this paper, we show how to fit different spatio-temporal models for disease mapping with INLA using the Leroux CAR prior for the spatial component, and we compare it with McMC using Kenya HIV incidence data during the period 2013-2016.

Stochastic Dynamics of Cholera Epidemic Model: Formulation, Analysis and Numerical Simulation

In this paper, we describe the two different stochastic differential equations representing cholera dynamics. The first stochastic differential equation is formulated by introducing the stochasticity to deterministic model by parametric perturbation technique which is a standard technique in stochastic modeling and the second stochastic differential equation is formulated using transition probabilities. We analyse a stochastic model using suitable Lyapunov function and Itôformula. We state and prove the conditions for global existence, uniqueness of positive solutions, stochastic boundedness, global stability in probability, moment exponential stability, and almost sure convergence. We also carry out numerical simulation using Euler-Maruyama scheme to simulate the sample paths of stochastic differential equations. Our results show that the sample paths are continuous but not differentiable (a property of Wiener process). Also, we compare the numerical simulation results for deterministic and stochastic models. We find that the sample path of SIsIaR-B stochastic differential equations model fluctuates within the solution of the SIsIaR-B ordinary differential equation model. Furthermore, we use extended Kalman filter to estimate the model compartments (states), we find that the state estimates fit the measurements. Maximum likelihood estimation method for estimating the model parameters is also discussed.

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.

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.