Browsing by Author "Kajunguri, Damian"

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Conservation of forest biomass and forest–dependent wildlife population: Uncertainty quantification of the model parameters
(Elsevier, 2023) Fanuel, Ibrahim; Mirau, Silas; Kajunguri, Damian; Moyo, Francis
The ecosystem is confronted with numerous challenges as a consequence of the escalating human population and its corresponding activities. Among these challenges lies the degradation of forest biomass, which directly contributes to a reduction in forested areas and poses a significant threat to the survival of wildlife species through the intensification of intraspecific competition. In this paper, a non–linear mathematical model to study the conservation of forest and wildlife species that are reliant on forest ecosystem within the framework of human population dynamics and its related activities is developed and analysed. The study assessed the impacts of economic measures in the form of incentives on reducing population pressure on forest resources as well as the potential benefits of technological efforts to accelerate the rate of reforestation. Qualitative and quantitative analyses reveals that economic and technological factors have the potential to contribute to resource conservation efforts. However, these efforts can only be used to a limited extent, and contrary to that, the system will be destabilised. Sensitivity analysis identified the parameters pertaining to human population, human activities, economic measures, and technological efforts as the most influential factors in the model
Conservation of forest biomass and forest–dependent wildlife population: Uncertainty quantification of the model parameters
(Elsevier, 2023-06) Fanuel, Ibrahim; Mirau, Silas; Kajunguri, Damian; Moyo, Francis
The ecosystem is confronted with numerous challenges as a consequence of the escalating human population and its corresponding activities. Among these challenges lies the degradation of forest biomass, which directly contributes to a reduction in forested areas and poses a significant threat to the survival of wildlife species through the intensification of intraspecific competition. In this paper, a non–linear mathematical model to study the conservation of forest and wildlife species that are reliant on forest ecosystem within the framework of human population dynamics and its related activities is developed and analysed. The study assessed the impacts of economic measures in the form of incentives on reducing population pressure on forest resources as well as the potential benefits of technological efforts to accelerate the rate of reforestation. Qualitative and quantitative analyses reveals that economic and technological factors have the potential to contribute to resource conservation efforts. However, these efforts can only be used to a limited extent, and contrary to that, the system will be destabilised. Sensitivity analysis identified the parameters pertaining to human population, human activities, economic measures, and technological efforts as the most influential factors in the model
Mass transfer approach and the designing of horizontal subsurface flow constructed wetland systems treating waste stabilisation pond effluent
(IWA Publishing, 2018-11-29) Rugaika, Anita; Kajunguri, Damian; Deun, Rob; Bruggen, Bart; Njau, Karoli
Pilot-scale constructed wetlands (CWs) that allowed wastewater to flow with high interstitial velocities in a controlled environment were used to evaluate the possibility of using mass transfer approach to design horizontal subsurface flow constructed wetlands (HSSF-CWs) treating waste stabilisation ponds (WSPs) effluent. Since CW design considers temperature which is irrelevant in tropics, mass transfer approach could improve the design. HSSF-CWs were operated in batch recycle mode as continuous stirred tank reactors (CSTR) at different interstitial velocities. The overall removal rate constants of chemical oxygen demand (COD) at various interstitial velocities were evaluated in mesocosms that received pretreated domestic wastewater. The mean overall removal rate constants were 0.43, 0.69, 0.74 and 0.73 d−1 corresponding to interstitial velocities of 15.43, 36, 56.57 and 72 md−1, respectively. Results showed that the interstitial velocities up to 36 md−1 represented a range where mass transfer effect was significant and, above it, insignificant to the COD removal process. Since WSPs effluent has high flow rates and low organic load, it is possible to induce high interstitial velocities in a HSSF-CW treating this effluent, without clogging and overflow. The performance of these HSSF for tertiary treatment in tropical areas could be improved by considering flow velocity when designing.
Mathematical model to study the impact of anthropogenic activities on forest biomass and forest-dependent wildlife population
(Springer Berlin Heidelberg, 2023-07-21) Fanuel, Ibrahim; Mirau, Silas; Kajunguri, Damian; Moyo, Francis
This paper proposes and analyses a nonlinear mathematical model to study the impact of anthropogenic activities on forest biomass and forest-dependent wildlife populations using a system of differential equations. It is assumed that the growth of forest biomass, forest-dependent wildlife populations, and the human population follow logistic equations. The effect of forest biomass depletion on the survival of forest-dependent wildlife populations is investigated by introducing a function that denotes the dependence on forest biomass. The system’s behaviour near all ecologically acceptable equilibria is studied, and to confirm the analytical conclusions, a numerical simulation is performed. The model analysis shows that as forest biomass declines due to an increase in human population and its associated activities, the population of wildlife species also declines, and if no measures are taken, both forest biomass and the wildlife population may become extinct.
Mathematical model to study the impact of anthropogenic activities on forest biomass and forest-dependent wildlife population
(Springer Berlin Heidelberg, 2023-07-21) Fanuel, Ibrahim; Mirau, Silas; Kajunguri, Damian; Moyo, Francis
This paper proposes and analyses a nonlinear mathematical model to study the impact of anthropogenic activities on forest biomass and forest-dependent wildlife populations using a system of differential equations. It is assumed that the growth of forest biomass, forest-dependent wildlife populations, and the human population follow logistic equations. The effect of forest biomass depletion on the survival of forest-dependent wildlife populations is investigated by introducing a function that denotes the dependence on forest biomass. The system’s behaviour near all ecologically acceptable equilibria is studied, and to confirm the analytical conclusions, a numerical simulation is performed. The model analysis shows that as forest biomass declines due to an increase in human population and its associated activities, the population of wildlife species also declines, and if no measures are taken, both forest biomass and the wildlife population may become extinct.
Mathematical Modeling on the Spread of Awareness Information to Infant Vaccination
(journal.sapub.org/am, 2015) Aminiel, Joram; Kajunguri, Damian; Mpolya, Emmanuel
In this paper, we examine the importance of spreading awareness information about infant vaccination in a population. A mathematical model for the spread of infant vaccination awareness information is proposed and analyzed quantitatively using the stability theory of the differential equations. The basic reproduction number 𝑅0 is obtained and its sensitivity analysis is carried out. The awareness free equilibrium is also proved to be locally and globally stable. Consideration is taken when 𝑅0 is greater than unity, which indicates that infant vaccination awareness information will invade the population and cause immunization to succeed. It is also proved that the maximum awareness equilibrium is locally stable if 𝑅0 is greater than unity. Numerical results show that word-of-mouth has a more impact on infant vaccination as compared to mass media, but better results are obtained by a combination of both word-of-mouth and mass media. For a successful infant vaccination programme, there is a need to emphasize both forms of awarenes.
Modeling and analysis of taeniasis and cysticercosis transmission dynamics in humans, pigs and cattle
(Springer Nature, 2021-03-19) Mwasunda, Joshua A.; Irunde, Jacob I.; Kajunguri, Damian; Kuznetsov, Dmitry
Taeniasis and cysticercosis pose a significant challenge to food safety and public health. Cysticercosis reduces the market value for pigs and cattle by making pork and beef unsafe for consumption. In this paper, a mathematical model for the transmission dynamics of taeniasis and cysticercosis in humans, pigs and cattle is formulated and analyzed. The analysis shows that both the disease free equilibrium (DFE) and the endemic equilibrium (EE) exist. To study the dynamics of the diseases, we derived the basic reproduction number R0 by next generation matrix method. When R0 < 1, the DFE is globally asymptotically stable whereas when R0 > 1 the EE is globally asymptotically stable. The normalized forward sensitivity index was used to determine sensitive parameters to the diseases. Humans’ recruitment rate, probability of humans’ infection with taeniasis and the defecation rate of taenia eggs by humans with taeniasis are the most positive sensitive parameters to diseases’ transmission whereas the human natural death rate is the most negative sensitive parameter. However, it is biologically unethical and not practical to increase human natural mortality rate for disease control. In this case, other parameters with negative sensitivity indices such as death rate of taenia eggs and proportions of unconsumed infected beef and pork can be considered for disease control. Generally, to control the diseases, more efforts should be made directed to reducing the number of humans who have taeniasis and defecate in the open environment. Also meat inspection and indoor keeping of cattle and pigs should be emphasized.
Modeling and Stability Analysis for Measles Metapopulation Model with Vaccination
(Science Publishing Group, 2015-10-22) Mpande, Leopard; Kajunguri, Damian; Mpolya, Emmanuel
In this paper, a metapopulation model is formulated as a system of ordinary differential equations to study the impact of vaccination on the spread of measles. The disease-free equilibrium is computed and proved to be locally and globally asymptotically stable if 1 C R < and unstable if 1 C R > . We show that when there are no movements between the two patches, there exists at least one endemic equilibrium for all 1 Ci R > and bifurcation analysis of endemic equilibrium point proves that forward (supercritical) bifurcation occurs in each patch. Numerical simulation results are also presented to validate analytical results and to show the impact of vaccination on the incidence and prevalence of measles in a metapopulation.
Modelling the Impact of Human Population and Its Associated Pressure on Forest Biomass and Forest-Dependent Wildlife Population
(Hindawi Limited, 2023-01-12) Fanuel, Ibrahim; Kajunguri, Damian; Moyo, Francis
Mathematical models have been widely used to explain the system originating from human-nature interaction, investigate the impacts of various components, and forecast system behaviour. This paper provides a profound reference to the current state of the art regarding the application of mathematical models to study the impact of human population and population pressure on forest biomass and forest-dependent wildlife. The review focused on two aspects, namely, model formulation and model analysis. In model formulation, the review revealed that socioeconomic status influences forest resource consumption patterns, thus, stratification of the human population based on economic status is a critical phenomenon in modelling human-nature interactions; however, this component has not been featured in the reviewed models. Regarding model analysis, in most of the reviewed work, single parameter approach was utilized to perform uncertainty quantification of the model parameter; this approach has been proven to be inadequate in measuring the uncertainty and sensitivity of the parameter. Thus, the use of correlation or variance based methods, which are multidimensional parameter space methods are of significant importance. Generally, despite the limitations of many assumptions in mathematical modelling, it is revealed that mathematical models demonstrate the ability to handle complex systems originating from interactions between humans and nature.