Modeling the Effect of Stress and Stigma on the Transmission and Control of Tuberculosis Infection

In this paper a continuous time deterministic model with health education campaign and treatment strategy is formulated to assess the effect of stress and stigma on the transmission and control of Tuberculosis (TB). The effective reproduction number is obtained and used to investigate the impact of health education campaign and treatment strategies. The effective reproduction numbers for health education campaign and treatment considered separately were found not to be effective as compared to a combination of both strategies. Numerical simulation results show that TB can be reduced or eliminated from the community when as treatment is applied. The disease prevalence and incidence are high when stigma is high and decline gradually when the combination of both treatment and health campaign are administered. We recommend that health education campaign to reduce stress among individuals and stigma for infectious individuals should be accompanied by treatment of active TB individuals for improved reduction of TB disease

Mathematical model to study the impact of anthropogenic activities on forest biomass and forest-dependent wildlife population

A project report submitted in International Journal of Dynamics and Control , Volume OnlineFirst – Jul 21, 2023This 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

Conservation of forest biomass and forest–dependent wildlife population: Uncertainty quantification of the model parameters

This research article was published by Heliyon 9 (2023)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 mode

Mass transfer approach and the designing of horizontal subsurface flow constructed wetland systems treating waste stabilisation pond effluent

This research article was published in Water Science and Technology Journal, Volume 78, Issue 12, 2018.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

Modeling and analysis of taeniasis and cysticercosis transmission dynamics in humans, pigs and cattle

This research article published by Springer Nature, 2021Taeniasis 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 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 the Control of Trypanosomiasis Using Trypanocides or Insecticide-Treated Livestock

In Uganda, cattle are an important reservoir for Trypanosoma brucei rhodesiense, the causative agent of Rhodesian sleeping sickness (human African trypanosomiasis), transmitted by tsetse flies Glossina fuscipes fuscipes, which feed on cattle, humans, and wild vertebrates, particularly monitor lizards. Trypanosomiasis can be controlled by treating livestock with trypanocides or insecticide – killing parasites or vectors, respectively. Mathematical modeling of trypanosomiasis was used to compare the impact of drug- and insecticide-based interventions on R0 with varying densities of cattle, humans and wild hosts. Intervention impact changes with the number of cattle treated and the proportion of bloodmeals tsetse take from cattle. R0 was always reduced more by treating cattle with insecticide rather than trypanocides. In the absence of wild hosts, the model suggests that control of sleeping sickness (R0<1) could be achieved by treating ∼65% of cattle with trypanocides or ∼20% with insecticide. Required coverage increases as wild mammals provide increasing proportion of tsetse bloodmeals: if 60% of non-human bloodmeals are from wild hosts then all cattle have to be treated with insecticide. Conversely, it is reduced if lizards, which do not harbor trypanosomes, are important hosts and/or if insecticides are used at a scale where tsetse numbers decline

Modelling the impact of TB superinfection on the dynamics of HIV-TB coinfection

Thesis (MSc (Mathematics))--University of Stellenbosch, 2009.ENGLISH ABSTRACT: In this thesis, a mathematical model describing the interaction between HIV and TB in the presence of TB superinfection is presented. The model takes into account two strains of Mycobacterium tuberculosis (MTB), where one strain is drug-sensitive and the other is resistant to at least one of the first-line anti-tuberculosis drugs. The impact of TB superinfection on the incidence and prevalence of TB in HIV-negative and HIVTB coinfected individuals is evaluated. Various control measures such as condom use, antiretroviral therapy, isoniazid preventive therapy and increased TB detection are studied using this model. Numerical results show that TB superinfection increases the prevalence and incidence of TB and its impact is more in HIV-negative than HIV-TB coinfected individuals. The results also show that TB superinfection promotes strain coexistence and increases the associated HIV mortality. Increased condom use was found to have a high positive impact towards the control of the two epidemics. Antiretroviral therapy decreases the TB notification rate and its impact on HIV prevalence increases with the coverage and efficacy. Isoniazid preventive therapy has a clear effect on the TB prevalence. Finally, increased TB detection was found to have a less impact on the TB incidence in HIV-TB coinfected individualsAFRIKAANSE OPSOMMING: In hierdie verhandeling word ´n wiskundige model vir die interaksie tussen MIV en TB, in ´n situasie met TB superinfeksie voorgelˆe. Die model neem twee variante van TB in ag. Een van die variante is sensitief vir MTB behandeling, terwyl die ander weerstandig is vir ten minste een van die eerste-linie TB behandenings. Die impak van TB superinfeksie op die insidensie and prevalensie van TB in MIV negatiewe en MIV-TB ko-ge˜ınfekteerde individu word ondersoek. Veskeie beheer maatreels soos kondoom gebruik, anti-retrovirale behandeling (vir MIV) en isonazid voorkomende behandeling en verhoodge TB deteksie (vir TB) word ondersoek. Numeriese resultate wys TB superinfeksie verhoog die prevalense en insidensie van TB en dat dit ´n groter bydrae maak by MIV negatief as by MIV-TB ko-geinfekteerde individu. Die resultate wys veder TB superinfeksie promofeer variant kohabitasie en verhoog MIV verwante mortalitieit. Verhoogde kondoom gebruik is gevind om ´n positiewe bydrae te maak tot die beheer van beide epidemies. Anti-retrovirale terapie verlaag die TB aanmeldings koers en die impak van ART verhoog saam met ´n verhoging in die dekking en effektiwiteit daarvan. Voorkomende behandeling het ´n beduidende impak op TB prevalensie. Ons vind dat TB deteksie ´n beperkte impak maak op TB insidensie by MIV-TB ko-geinfekteerde individ

Modelling the control of tsetse and African trypanosomiasis through application of insecticides on cattle in Southeastern Uganda

Thesis (PhD)--Stellenbosch University, 2013.ENGLISH ABSTRACT: In Uganda, cattle are an important reservoir of Trypanosoma brucei rhodesiense, a parasite that causes human African trypanosomiasis or sleeping sickness. We developed mathematical models to examine the transmission of T. b. rhodesiense by tsetse vector species, Glossina fuscipes fuscipes in a host population that consists of humans, domestic and wild mammals, and reptiles. The models were developed and analysed based on the situation in Tororo district in Southeastern Uganda, where sleeping sickness is endemic and which has a cattle and human population of 40, 000 and 500, 000, respectively. Assuming populations of cattle and humans only, the impact of mass chemoprophylaxis and vector control through insecticide-treated cattle (ITC) is evaluated. Keeping 12% or 82% of the cattle population on insecticides that have an insecticidal killing effect of 100% at all times or trypanocides that have 100% efficacy, respectively, can lead to the control of T. b. rhodesiense in both humans and cattle. Optimal control of T. b. rhodesiense is shown to be achieved through ITC alone or a combination of chemoprophylaxis and ITC, the former being the cheapest control strategy. Allowing for the waning effect of insecticides and including wildhosts, T. b. rhodesiense control can be achieved by keeping 21% or 27% of the cattle population on insecticides through whole-body or restricted application, respectively. Restricting the treatment of insecticides to adult cattle only would require 24% or 33% of the adult cattle population to be kept on insecticides through whole-body or restricted application, respectively, to control T. b. rhodesiense. A cost-effectiveness and benefit-cost analysis of using ITC to control T. b. rhodesiense show that restricted application of insecticides is a cheaper and more beneficial strategy compared to whole-body treatment. The results of the study show that the restricted application of insecticides on cattle provides a cheap, safe and farmer-based strategy for controlling tsetse and trypanosomiasis.AFRIKAANSE OPSOMMING: In Uganda is beeste ’n belangrike reservoir van Trypanosoma brucei rhodesiense, ’n parasiet wat tripanosomiase of slaapsiekte in mense veroorsaak. Ons het wiskundige modelle ontwikkel wat die oordrag van T. b. Rhodesiense deur tesetse vektor spesies, Glossina fuscipes fuscipes in ’n draer populasie wat bestaan uit mense, mak en wilde diere en reptiele, ondersoek. Die modelle was ontwikkel en geanaliseer gebaseer op die oordrag situasie in die Tororo distrik in Suidoostelike Uganda, ’n gebied waar slaapsiekte endemies is en wat ’n populasie van 40, 000 beeste en 500, 000 mense het. Die impak van massa chemoprofilakse en vektor beheer deur insekdoder-behandelde beeste is gevalueer onder die aanname van bees en mens populasies alleenlik. Beheer oor T. b. Rhodesiense in beide mense en beeste kan verkry word deur of 12% van die bees populasie te behandel met ’n insekdoder wat 100% effektief is ten alle tye of 82% van die bees populasie te behandel met tripanosiedes wat 100% effektief is. Daar is aangetoon dat optimale beheer van T. b. Rhodesiense bereik kan word deur die gebruik van insekdoders alleenlik of ’n kombinasie van insekdoders en chemoprofilakse, hoewel eersgenoemde die goedkoopste strategie is. Wanneer die kwynende effek van insekdoders asook wilde diere as draers in ag geneem word, kan T. b. Rhodesiense beheer verkry word deur 21% van beeste se hele liggaam met insekdoders te behandel of 27% gedeeltelik te behandel. As slegs volwasse beeste met insekdoders behandel word, moet 24% se hele liggaam of 33% gedeeltelik behandel word vir beheer van T. b. Rhodesiense. ’n Koste-effektiwiteit en voordeel-koste analise van insekdoders as beheermaatstaf vir T. b. Rhodesiense toon aan dat gedeeltelike behandeling van die bees se liggaam die goedkoper en meer voordelige strategie is in vergelyking met behandeling van die hele liggaam. Die resultate van die studie wys dat gedeeltelike behandeling van beeste met insekdoders ’n goedkoop, veilige en landbouer-gebaseerde strategie is om tsetse en tripanosomiase te beheer

Mathematical Modeling on the Spread of Awareness Information to Infant Vaccination

Research Article published by journal.sapub.org/amIn 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 0 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 0 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 0 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

Irrigation water allocation optimization using multi-objective evolutionary algorithm (MOEA) − a review

This paper analyzes more than 40 papers with a restricted area of application of Multi-Objective Genetic Algorithm, Non-Dominated Sorting Genetic Algorithm-II and Multi-Objective Differential Evolution (MODE) to solve the multi-objective problem in agricultural water management. The paper focused on different application aspects which include water allocation, irrigation planning, crop pattern and allocation of available land. The performance and results of these techniques are discussed. The review finds that there is a potential to use MODE to analyzed the multi-objective problem, the application is more significance due to its advantage of being simple and powerful technique than any Evolutionary Algorithm. The paper concludes with the hopeful new trend of research that demand effective use of MODE; inclusion of benefits derived from farm byproducts and production costs into the model