Browsing by Author "Mbalawata, Isambi"

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A two-patch model to quantify uncertainties in the transmission of brucellosis between domestic animals
(Elsevier, 2025-09) Msuya, Rehema; Mirau, Silas; Nyerere, Nkuba; Mbalawata, Isambi
Brucellosis, a neglected zoonotic disease, poses significant health risks to both humans and livestock. This study investigates a key factor influencing brucellosis transmission: the movement of animals in and out of communal grazing areas. We develop a Continuous Time Markov Chain (CTMC) stochastic model, building on its deterministic counterpart, to assess the impact of short-term animal movements on disease transmission dynamics. By incorporating stochasticity, the model captures the inherent variability in disease transmission and animal movements, providing deeper insights than traditional deterministic models. A multitype branching process is employed to evaluate the probabilities of disease extinction. We compute the basic reproduction number and the stochastic threshold . Numerical simulations indicate that brucellosis transmission accelerates when domestic animals spend more time in high-risk communal grazing areas. Additionally, the results suggest a high probability of disease extinction when animals moves out of high-risk area. Conversely, when animals from both patches increase their time in high-risk zones, the likelihood of disease extinction diminishes. This study underscores the importance of implementing strategic movement controls and targeted interventions in high-risk areas to mitigate outbreaks and enhance disease management.
Bayesian prediction of under-five mortality rates for Tanzania
(Elsevier Inc., 2025-01-26) Mwanga, Mohamed; Mirau, Silas; Tchuenche, Jean; Mbalawata, Isambi
Under-five mortality is a burden on health and economic systems in developing countries. This study used under-five mortality rate (U5MR) data for Tanzania from 1960 to 2020 to predict trends of under-five mortality over the period of 2021 to 2051. Using a Bayesian state space model, it is found that the model is stable in forecasting. Results show that under-five mortality will continue to decline from 48.9 in 2020 to 32.9 in 2030, a decrease of 32.7%. But despite this decrease, Tanzania will likely not meet the Sustainable Development Goal (SDG) for under-five mortality by 2030. Additional efforts by the government through evidence-based interventions should be undertaken to improve child survival by expanding access to health care, especially in rural areas, taking into account local context.
Ecological modeling for the dynamics of potato tuber moth in Irish potatoes biomass
(Elsevier, 2025-09) Sanga, Luta; Masanja, Verdiana; Mbalawata, Isambi
The Potato Tuber Moth (Phthorimaea operculella) threatens food security and livelihoods in developing nations, especially for smallholder farmers dependent on Irish potatoes (Solanum tuberosum L.). This study has developed a non-linear deterministic ecological model to analyze the moth's dynamics in Irish potatoes biomass with deployment of predators and farming campaigns aiming to minimize Moth population growth and enhance Irish potato harvest. The model analysis demonstrates that the coexistence equilibrium point is globally asymptotically stable, as evidenced by phase portraits. To validate the model, parameter estimation and model fitting were conducted using non-linear least squares. Furthermore, a global sensitivity analysis was carried out using Latin Hypercube Sampling to determine the most influential parameters affecting the system's behavior. Numerical simulations reveals that Integrated Pest Management (IPM) strategies, combining predators and farming campaigns, effectively reduced pest populations while maximizing potato yields to approximately 100 tubers per square meter, compared to sub-optimal yields of 33 tubers per square meter with predators alone. This study recommends IPM strategies as a good approach to minimize Potato Tuber Moth (PTM) and optimize Irish potatoes yields.
Mathematical Approach to Investigate Stress due to Control Measures to Curb COVID-19
(Hindawi, 2022-01-13) Paul, James; Mirau, Silas; Mbalawata, Isambi
COVID-19 is a world pandemic that has affected and continues to affect the social lives of people. Due to its social and economic impact, different countries imposed preventive measures that are aimed at reducing the transmission of the disease. Such control measures include physical distancing, quarantine, hand-washing, travel and boarder restrictions, lockdown, and the use of hand sanitizers. Quarantine, out of the aforementioned control measures, is considered to be more stressful for people to manage. When people are stressed, their body immunity becomes weak, which leads to multiplying of coronavirus within the body. Therefore, a mathematical model consisting of six compartments, Susceptible-Exposed-Quarantine-Infectious-Hospitalized-Recovered (SEQIHR) was developed, aimed at showing the impact of stress on the transmission of COVID-19 disease. From the model formulated, the positivity, bounded region, existence, uniqueness of the solution, the model existence of free and endemic equilibrium points, and local and global stability were theoretically proved. The basic reproduction number () was derived by using the next-generation matrix method, which shows that, when , the disease-free equilibrium is globally asymptotically stable whereas when the endemic equilibrium is globally asymptotically stable. Moreover, the Partial Rank Correlation Coefficient (PRCC) method was used to study the correlation between model parameters and . Numerically, the SEQIHR model was solved by using the Rung-Kutta fourth-order method, while the least square method was used for parameter identifiability. Furthermore, graphical presentation revealed that when the mental health of an individual is good, the body immunity becomes strong and hence minimizes the infection. Conclusively, the control parameters have a significant impact in reducing the transmission of COVID-19.
Mathematical modeling of COVID-19 transmission dynamics between healthcare workers and community
(Elsevier, 2021-10) Masandawa, Lemjini; Mirau, Silas; Mbalawata, Isambi
Corona-virus disease 2019 (COVID-19) is an infectious disease that has affected different groups of humankind such as farmers, soldiers, drivers, educators, students, healthcare workers and many others. The transmission rate of the disease varies from one group to another depending on the contact rate. Healthcare workers are at a high risk of contracting the disease due to the high contact rate with patients. So far, there exists no mathematical model which combines both public control measures (as a parameter) and healthcare workers (as an independent compartment). Combining these two in a given mathematical model is very important because healthcare workers are protected through effective use of personal protective equipment, and control measures help to minimize the spread of COVID-19 in the community. This paper presents a mathematical model named SWE 𝐼𝑠 𝐼𝑎HR; susceptible individuals (S), healthcare workers (W), exposed (E), symptomatic infectious (𝐼𝑠 ), asymptomatic infectious (𝐼𝑎 ), hospitalized (H), recovered (R). The value of basic reproduction number 𝑅0 for all parameters in this study is 2.8540. In the absence of personal protective equipment 𝜉 and control measure in the public 𝜃, the value of 𝑅0 ≈ 4.6047 which implies the presence of the disease. When 𝜃 and 𝜉 were introduced in the model, basic reproduction number is reduced to 0.4606, indicating the absence of disease in the community. Numerical solutions are simulated by using Runge–Kutta fourth-order method. Sensitivity analysis is performed to presents the most significant parameter. Furthermore, identifiability of model parameters is done using the least square method. The results indicated that protection of healthcare workers can be achieved through effective use of personal protective equipment by healthcare workers and minimization of transmission of COVID-19 in the general public by the implementation of control measures. Generally, this paper emphasizes the importance of using protective measures.
Mathematical modeling of vaccination as a control measure of stress to fight COVID-19 infections
(Elsevier, 2023-01) Paul, James; Mbalawata, Isambi; Mirau, Silas; Masandawa, Lemjini
The world experienced the life-threatening COVID-19 disease worldwide since its inversion. The whole world experienced difficult moments during the COVID-19 period, whereby most individual lives were affected by the disease socially and economically. The disease caused millions of illnesses and hundreds of thousands of deaths worldwide. To fight and control the COVID-19 disease intensity, mathematical modeling was an essential tool used to determine the potentiality and seriousness of the disease. Due to the effects of the COVID-19 disease, scientists observed that vaccination was the main option to fight against the disease for the betterment of human lives and the world economy. Unvaccinated individuals are more stressed with the disease, hence their body’s immune system are affected by the disease. In this study, the 𝑆𝑉 𝐸𝐼𝐻𝑅 deterministic model of COVID- 19 with six compartments was proposed and analyzed. Analytically, the next-generation matrix method was used to determine the basic reproduction number (𝑅0). Detailed stability analysis of the no-disease equilibrium (𝐸0) of the proposed model to observe the dynamics of the system was carried out and the results showed that 𝐸0 is stable if 𝑅0 < 1 and unstable when 𝑅0 > 1. The Bayesian Markov Chain Monte Carlo (MCMC) method for the parameter identifiability was discussed. Moreover, the sensitivity analysis of 𝑅0 showed that vaccination was an essential method to control the disease. With the presence of a vaccine in our 𝑆𝑉 𝐸𝐼𝐻𝑅 model, the results showed that 𝑅0 = 0.208, which means COVID-19 is fading out of the community and hence minimizes the transmission. Moreover, in the absence of a vaccine in our model, 𝑅0 = 1.7214, which means the disease is in the community and spread very fast. The numerical simulations demonstrated the importance of the proposed model because the numerical results agree with the sensitivity results of the system. The numerical simulations also focused on preventing the disease to spread in the community
Mathematical models for aflatoxin contamination in crops, livestock and humans: A review
(SCIK Publishing Corporation, 2022-11-07) Mgandu, Filimon; Ngailo, Triphonia; Mugume, Isaac; Mbalawata, Isambi; Mirau, Silas
Aflatoxin is among the highest-threatening food contaminants as it affects both the health of consumers and the entire value chain. Researchers are of the view that aflatoxin contamination will increase due to the impacts of climate change. This study aimed to review studies on modelling the impacts of climate change on aflatoxin contamination to gain a deeper understanding of the progress achieved, methodologies used and potential gaps or opportunities for further studies. A critical analysis of the available literature revealed that aflatoxin contamination is a spatial-temporal phenomenon as it depends on both location and time. In many regions, data unavailability has been an obstacle in developing predictive models. We note that it is necessary for each region to have their own models according to the crop, soil characteristics and projected climate of the given area for better and more accurate results. Future studies should focus on the first; surveillance of susceptible crops and gathering of aflatoxin contamination data. Second, developing models to assess the aflatoxin contamination risk due to projected climate change, soil properties, and crop characteristics so that proper strategies can be adopted. Third, laboratory experimental results must be validated in fields to increase their usability.
Modeling nosocomial infection of COVID-19 transmission dynamics
(Elsevier, 2022-06) Masandawa, Lemjini; Mirau, Silas; Mbalawata, Isambi; Paul, James; Kreppel, Katharina; Msamba, Oscar
COVID-19 epidemic has posed an unprecedented threat to global public health. The disease has alarmed the healthcare system with the harm of nosocomial infection. Nosocomial spread of COVID-19 has been discovered and reported globally in different healthcare facilities. Asymptomatic patients and super-spreaders are sough to be among of the source of these infections. Thus, this study contributes to the subject by formulating a 𝑆𝐸𝐼𝐻𝑅 mathematical model to gain the insight into nosocomial infection for COVID-19 transmission dynamics. The role of personal protective equipment 𝜃 is studied in the proposed model. Benefiting the next generation matrix method, 𝑅0 was computed. Routh–Hurwitz criterion and stable Metzler matrix theory revealed that COVID-19-free equilibrium point is locally and globally asymptotically stable whenever 𝑅0 < 1. Lyapunov function depicted that the endemic equilibrium point is globally asymptotically stable when 𝑅0 > 1. Further, the dynamics behavior of 𝑅0 was explored when varying 𝜃. In the absence of 𝜃, the value of 𝑅0 was 8.4584 which implies the expansion of the disease. When 𝜃 is introduced in the model, 𝑅0 was 0.4229, indicating the decrease of the disease in the community. Numerical solutions were simulated by using Runge–Kutta fourth order method. Global sensitivity analysis is performed to present the most significant parameter. The numerical results illustrated mathematically that personal protective equipment can minimizes nosocomial infections of COVID-19.
Posterior Distribution of the Unknown Parameter of Poisson Distribution Under Different Priors: An Application to Under-Fivemortality Data
(SSRN, 2023-03-30) Mwanga, Mohamed; Tchuenche, Jean; Mirau, Silas; Mbalawata, Isambi
Under-five mortality rate is one of the most essential indicator of acountry’s socio-economic well-being and public health status. Poissondistribution under different priors such as conjugate/Gamma prior,uniform and Jeffrey’s prior is used to obtain posterior distribution ofthe unknown parameter with an application to under-five mortalitydata in six East Africa countries from 1960 to 2020. The estimatesare examined through a Bayesian analysis while all the calculationsare carried out the R-statistical software and MS Excel. Among allpriors used in this study, conjugate prior was found to be compatiblefor the unknown parameters of the Poisson distribution. The casesof under-five mortality are found to reduce over time. East Africacountries through East Africa Community (EAC) should build strongand resilient health systems, identify and prioritize interventions tomitigate under-five mortality among Member States.
Posterior Distribution of the Unknown Parameter of Poisson Distribution Under Different Priors: An Application to Under-Fivemortality Data
(Elsevier Inc, 2023-04-23) Mwanga, Mohamed; Tchuenche, Jean; Mirau, Silas; Mbalawata, Isambi
Under-five mortality rate is one of the most essential indicator of acountry’s socio-economic well-being and public health status. Poissondistribution under different priors such as conjugate/Gamma prior,uniform and Jeffrey’s prior is used to obtain posterior distribution ofthe unknown parameter with an application to under-five mortalitydata in six East Africa countries from 1960 to 2020. The estimatesare examined through a Bayesian analysis while all the calculationsare carried out the R-statistical software and MS Excel. Among allpriors used in this study, conjugate prior was found to be compatiblefor the unknown parameters of the Poisson distribution. The casesof under-five mortality are found to reduce over time. East Africacountries through East Africa Community (EAC) should build strongand resilient health systems, identify and prioritize interventions tomitigate under-five mortality among Member States.
Sensitivity analysis and uncertainty quantification of climate change effects on Tanzanian banana crop yield
(Elsevier B. V., 205-01-09) Patrick, Sabas; Mirau, Silas; Mbalawata, Isambi; Leo, Judith
Concerns about the impact of climate change on agricultural systems have heightened, par ticularly in regions where crop cultivation is essential for economic stability and sustenance. This research addresses a critical gap in understanding by investigating how climate change influences Tanzania’s bananas, a vital component of the country’s agricultural sector. The study used a multiple regression model to analyze the correlation between bananas and key climate variables in Tanzania, the results showed gradual decrease in bananas. Specifically, the climate variables, including precipitation (𝑋1), soil moisture (𝑋2), minimum temperature (𝑋3), maximum temperature (𝑋4), and relative humidity (𝑋5) have coefficients 0.0206, −0.0085, 4.8328, −1.6594, and −0.0991, respectively. In this case, a large positive coefficient and a negligible negative coefficient show that the independent variable greatly influences the yield of the bananas. Additionally, the study utilize two powerful global sensitivity analysis methods, Sobol’ Sensitivity Indices and Response Surface Methodology, to comprehensively explore the sensitivity of bananas to climate variables. So, these methods revealed that minimum temperature, precipitation and soil moisture have the most impact on bananas and affect the crop’s production variability. Uncertainty quantification was performed using Monte Carlo simulation, estimating uncertainties in model parameters to enhance the reliability of the findings. This research not only contributes to our broader understanding of how climate change impacts bananas but also offers practical policy suggestions tailored to Tanzania’s unique context, ensuring resilience and sustainability in the face of environmental changes. The outcomes of this study carry significance for policymakers, stakeholders, and farmers, providing actionable insights to shape adaptive agricultural strategies. By bridging the gap between climate change and bananas
Soil-Transmitted Helminthiasis Control Strategies
(CC-BY 4.0 International license, 2025-08-06) Masandawa, Lemjini; Amadi, Miracle; Mbalawata, Isambi; Kinung, Safari; Mirau, Silas
Soil-transmitted helminthiasis (STH) is a parasitic disease that affects over 1.5 billion people worldwide. The use of mathematical models to inform time-bound projections and support WHO targets is growing. Never- theless, there is a lack of comprehensive synthesis regarding the extent to which mathematical frameworks for STH control account for the timeframe and effectiveness of interventions required to meet WHO programmatic goals.
Time Series Analysis of Economic Factors Influencing Deforestation in Tanzania
(Journal of Mathematics and Informatics, 2023-02-28) Gweba, John; Mbalawata, Isambi
Climate change is a significant contributor to environmental harm and the rise in Atmospheric carbon dioxide, which raises the earth’s surface temperature. As forests are the primary mechanism for absorbing carbon dioxide gas and protecting the earth from global warming and unpredictable weather patterns, a high rate of deforestation is to blame for this. In this study, the economic drivers causing deforestation in Tanzania include per capita income, per capita purchasing power, inflation rate, per capita purchasing power, poverty rate, and electricity consumption are investigated. Autoregressive models with exogenous variables (VARX (1) – VARX (3)) models are formulated to analyze the effect of economic variables and forecast the rate of deforestation in Tanzania. The time series data used from 1994 to 2014 were collected in Tanzania, nature of the data suggests the increase in the rate of deforestation as time progresses. In this study, the best model VARX (3, 0) was obtained, and the relationship between the variables through granger causality was obtained. Also, forecasting was carried out for the next 10 years using the best model VARX (3, 0) and Kalman Filters. It was observed that economic variables, especially the poverty rate, have an impact on the rate of deforestation in Tanzania. Furthermore, the graph shows the increasing trend in the rate of deforestation in the coming years in Tanzania.
Time series and ensemble models to forecast banana crop yield in Tanzania, considering the effects of climate change
(Elsevier, 2023-12-01) Patrick, Sabas; Mirau, Silas; Mbalawata, Isambi; Leo, Judith
Banana cultivation plays a pivotal role in Tanzania’s agricultural landscape and food security. Precisely forecasting banana crop yield is essential for resource optimization, market stability, and informed policymaking, particularly in the face of climate change. This study employed time series and ensemble models to forecast banana crop yield in Tanzania, offering crucial insights into future production trends. We utilized Seasonal ARIMA with Exogenous Variables (SARIMAX), State Space (SS), and Long Short-Term Memory (LSTM) models, chosen based on regression analysis and data exploration. Leveraging historical banana yield data (1961–2020) and relevant climate variables, we formulated an ensemble model using a weighted average approach. Our findings underscore the potential of time series and ensemble models for accurate banana crop yield forecasting. Statistical evaluation metrics validate their effectiveness in capturing temporal variations and delivering reliable predictions. This research advances agricultural forecasting by demonstrating the successful application of these models in Tanzania. It emphasizes the importance of considering temporal dynamics and relevant factors for precise predictions. Policymakers, farmers, and stakeholders can leverage this study’s outcomes to make informed decisions on resource allocation, market planning, and agricultural policies. Ultimately, our research bolsters sustainable banana production and enhances food security in Tanzania.