Hepatitis B Virus Disease: A Mathematical Model for Vertical Transmission with Treatment Strategy

This paper presents a mathematical model that captures some essential information about the impacts of treatment on hepatitis B vertical transmission. The treatment induced reproduction number is compared with the basic reproduction number to assess the possible benefits to be obtained from this control measure. Numerical results and sensitivity analysis are carried out to support the analytical results and determine the parameters influencing the dynamics of the disease. It is indicated that in the presence of treatment, transmission of infection decreases, implying that the number of acute and chronic infected adult women decrease as well, resulting into fewer infected newborn babies.   Mathematics Subject Classification: 34D20 Key words: Hepatitis B virus, vertical transmission, treatment, reproduction numbe

Impacts of rainfall and temperature variation on maize (Zea mays L.) yields: A case study of Mbeya Region, Tanzania

Based on the multiple regression model the impacts of rainfall and temperature on maize (Zea mays L.) yields in Mbeya region have been analyzed. Overall, findings revealed that the seven selected variables, that is, January maximum temperature, February maximum temperature, April maximum temperature, Rainfall from February to April, Rainfall during growing season, December rainfall and October maximum temperature influenced maize yields in the region by 65.4%. Diversely, the results showed 34.6% wasn’t explained by the model, meaning that there are other factors apart from temperature and rainfall could be used to explain the variation of maize (Z. mays) yield in the region. Furthermore, taking 1990 -2012 as baseline period, the model projection for a period of 2020-2042 shows that maize (Z. mays) yield may change from 1.5% to 2.3%, 2.6% to 3.6% and 2.4% to 3.5 %, as a result of separate future influence of 10% decrease in rainfall, 10C raise in temperature and combined influence of both temperature and rainfall change, respectively. Nevertheless, the findings from this study, reveals that Mbeya region may still be potential maize (Z. mays) growing region in the prescribed period provided the magnitude change of both future rainfall and temperature hold and other factors not explained by the model do not change significantly. Therefore, the government must focus to conduct more research on uses of appropriate maize (Z. mays) varieties to obtain the maximum maize (Z. mays) crop yield in the region

Risk Factors Associated with Mother-to-Child Transmission of HIV in Dar es Salaam, Tanzania

Despite Tanzania's efforts and substantial progress in PMTCT, about 11% new infections were recorded among Tanzanian children in 2019 (UNAIDS 2020a). The objective of this study was to determine the rate of HIV transmission and to identify its risk factors among HIV exposed infants born to HIV-positive mothers in Dar es Salaam, Tanzania. A cross-sectional study was conducted using retrospective data collected from HIV-positive mothers and their exposed babies who were followed and registered in health facilities in four administrative districts (Ilala, Temeke, Kinondoni, and Ubungo) in Dar es Salaam between January 2016 and December 2019.  To identify risk factors for MTCT, univariate and multivariate Cox Proportional hazard regression analyses were employed. Out of 18705 registered children exposed to HIV, 586 (3.1%) were positive during the study period, while 18119 (96.9%) were negative. In this study, the following factors were increasing the risks of MTCT of HIV infections, not receiving ARV prophylaxis right at birth (aHR = 2.39, 95% CI: 1.75–3.26, P < 0.001), unsuppressed maternal viral load (aHR = 6.26, 95% CI: 4.91–7.97, P < 0.001), WHO clinical stage 3–4 (aHR = 1.79, 95% CI: 1.44–2.23, P < 0.001), and mixed feeding (aHR = 4.09, 95% CI: 1.80–9.31, P < 0.001). The factors maternal age group 25–34 years (aHR = 0.47, 95% CI: 0.29–0.75, P < 0.001), being married/cohabiting (aHR = 0.47, 95% CI: 0.23–0.95, P = 0.036), duration on ART for > 12 months (aHR = 0.55, 95% CI: 0.45–0.67, P < 0.001), dried blood spot (DBS) tested at 6 weeks (aHR = 0.09, 95% CI: 0.04–0.18, P < 0.001), and exclusive replacement feeding (ERF) (aHR = 0.32, 95% CI: 0.17–0.60, P < 0.001) decreased the risk of MTCT of HIV infections. These findings indicated that further work is required to scale up PMTCT approaches to concentrate on viral load suppression, taking ARV prophylaxis immediately at birth, and EBF practice in the first 6 months of life. Keywords: HIV, PMTCT, risk factors, mother-to-child transmission (MTCT)

Statistical Analysis of Ambient Conditions and Water Temperature on Standard Achievement of Volume Calibration of Small Laboratory Glassware

Volumetric apparatus calibration is a very sensitive matter in metrological institutions. Identification and evaluation of the uncertainty factors affecting volume calibration of volumetric apparatus such as small laboratory glassware is a critical issue to investigate in order to increase accuracy in calibration. This study investigates the contributions of ambient conditions and water temperature in volume calibration of small laboratory glassware. The study used existing empirical data from the Tanzania Bureau of Standards. The multiple linear regression model was used to establish better relationship between explanatory variables and response variable. The model analyzed three predictor variables namely ambient temperature, pressure and relative humidity. Water temperature was dropped due to high multicollinearity with ambient temperature. The results from this study revealed that the variations in calibration of small volumetric laboratory glassware have strong association with ambient temperature, pressure and their interaction and weak one with ambient relative humidity. It is therefore recommended to have appropriate settings of these ambient conditions in volume calibration of small laboratory glassware to ensure that the glassware used for analysis and other practices are accurately calibrated for betterment of practical or test results.Keywords: Calibration; ambient conditions; small laboratory glassware; uncertainty factors

Sensitivity Analysis and Uncertainty Parameter Quantification in a Regression Model: The Case of Deforestation in Tanzania

Sep 2020, Published Oct 2020AbstractIn this paper a multiple regression model for the economic factors and policy that influence therate of deforestation in Tanzania is formulated. Sensitivity analysis for parameters of explanatoryvariables using one-at-a time and direct methods is carried out and the model is fitted by classicalleast square (LSQ) and Markov Chain Monte Carlo (MCMC) methods. Uncertainty quantificationof parameters by adaptive Markov Chain Monte Carlo methods is performed. The coefficient ofdetermination indicates that 87% of deforestation rate is explained by explanatory variablescaptured in the model. Household poverty rate is found to be the most sensitive factor todeforestation, while purchasing power is the least sensitive in both methods. Model validationindicates a good agreement between the collected data and the predicted data by the model andMarkoc Chain Monte Carlo method yielded a good sample mix. Thus, the study recommends thatsince economic activities tend to increase the rate of deforestation, then policy and decisionmakingprocesses should link the country’s desire for economic growth and environmentalmanagement. Keywords: deforestation; economic factors; Markov Chain Monte Carlo methods; regressionmodel; sensitivity

Modelling and Analysis of a Holling Type II Stage Structured Predator-Prey System in the Presence of Harvesting

The effect of harvesting and predation on a Holling type II stage-structured predator-prey system with assumption that harvesting and predation happen only to mature preys was investigated. Stability of interior point was analysed using Routh Hurwith Criterion. Numerical simulations were carried out. The results show that harvesting and predation have strong negative impacts on population dynamics of stage structured predator-prey system.Keywords: Predator-prey System; Stage Structure; Holling type II; Harvestin

The Use of Non-Standard Finite Difference Schemes to Solve the DAMP and SIT Models

Abstract Sterile insect technique (SIT) is a method of biological control that uses sterile male insects to reduce the reproductive rate of a species of target insect. The method relies on the release of sterile or treated males in order to reduce the native population of insects. We propose the model that governs the dynamics of the anopheles mosquito population, and then modify to incorporate the sterile insect technique as an intervention to curtail the reproduction of mosquitoes. The nonstandard finite difference numerical schemes and simulations for these models are provided. The results indicate that sterile technique with frequent and high rate of release can be an alternative to chemical control tools in the fight against malaria

Optimal Control of Shigellosis with Cost-Effective Strategies

In this paper, we apply optimal control theory to the model for shigellosis. It is assumed that education campaign, sanitation, and treatment are the main controls for this disease. The aim is to minimize the number of infections resulting from contact with careers, infectious population, and contaminated environments while keeping the cost of associated controls minimum. We achieve this aim through the application of Pontryagin’s Maximum Principle. Numerical simulations are carried out by using both forward and backward in time fourth-order Runge-Kutta schemes. We simulate the model under different strategies to investigate which option could yield the best results. The findings show that the strategy combining all three control efforts (treatment, sanitation, and education campaign) proves to be more beneficial in containing shigellosis than the rest. On the other hand, cost-effectiveness analysis is performed via incremental cost-effectiveness ratio (ICER). The findings from the ICER show that a strategy incorporating all three controls (treatment, sanitation, and education campaign) is the most cost-effective of all strategies considered in the study