Mathematical models for effectiveness of contact tracing on the onset of an epidemic

Paper presented at Strathmore International Math Research Conference on July 23 - 27, 2012Paper presented at Strathmore International Mathematics Research Conference on July 23 - 27, 201

A Mathematical model for the dynamics and control of river blindness with asymptomatic infected humans

Paper presented at the 5th Strathmore International Mathematics Conference (SIMC 2019), 12 - 16 August 2019, Strathmore University, Nairobi, KenyaOnchocerciasis, also known as river blindness, is a disease caused by infection with SBS the parasitic worm Onchocerca volvulus and is transmitted to humans through exposure to repeated bites of infected blackflies of the genus Simulium. It is endemic mostly in remote and rural areas in sub-Saharan Africa. Community-directed annual mass drug administration (MDA) with ivermectin is the core to eliminate onchocerciasis in all endemic foci in Africa. However, novel and alternative strategies such as vaccination are urgently required to supplement elimination of the disease. In this study, a mathematical model with asymptomatic infected humans is formulated to assess the impact of the different control strategies. Model analysis is performed for the existence and stability of the equilibrium points. The next generation approach is used to calculate the basic reproduction number, Ro. The disease-free equilibrium (DFE) is locally asymptotically stable when Ro < 1. The study findings reveal that a combination of mass treatment s with ivermectin together with vaccination should be applied to eliminate the disease.Mbaruru University of Science and Technology, Uganda

A Mathematical model for bovine brucellosis incorporating contaminated environment

Paper presented at Strathmore International Math Research Conference on July 23 - 27, 201

Modeling and stability analysis of the African swine fever epidemic model

Paper presented at the 5th Strathmore International Mathematics Conference (SIMC 2019), 12 - 16 August 2019, Strathmore University, Nairobi, KenyaIn this paper, a mathematical model for the transmission dynamics and control of African swine fever with recruitment of susceptible, exposed and infective domestic pigs into the population is studied using a system of ordinary differential equations. The basic reproduction number Ro for the model was obtained and its dependence on model parameters discussed. Without the inflow of exposed and infective pigs into the population, the model exhibits the disease-free equilibrium Eo and the endemic equilibrium El. The disease-free equilibrium Eo is globally stable if the basic reproduction number Ro < 1 and the disease will be wiped out of the population. If Ro > 1, the endemic equilibrium El is asyrnptotically globally stable and the disease persists in the population. With the influx of exposed and infective domestic pigs, the model has only a unique endemic equilibrium Ee that is globally asymptotically stable and the disease persists. Numerical simulation is carried out to verify the analytical results. It is revealed that with the influx of the exposed and infected pigs, the disease is maintained at endemic equilibrium.Mbarara University of Science and Technology, Uganda

Modelling transmission and control of African Swine Fever in Uganda with transportation of infected pigs

Paper presented at the 4th Strathmore International Mathematics Conference (SIMC 2017), 19 - 23 June 2017, Strathmore University, Nairobi, Kenya.African Swine Fever (ASF) is a devastating haemorrhagic fever of pigs that causes up to 100% mortality, for which there is no vaccine and treatment. Its highly contagious nature and ability to spread over long distances make it one of the most feared diseases, since it’s devastating effects on pig production have been experienced most of sub-Saharan Africa. A mathematical model for spread and control of African Swine Fever with and without transportation of infected pigs is studied using a system of ordinary differential equations. Model analysis is carried out for existence and stability of the equilibrium points to establish the long time behavior of the disease. It is revealed that without inflow of infected pigs into the population, the model has both the disease free and the endemic equilibrium points. The disease free equilibrium point is globally stable when the basic reproduction number is less than one and the disease can be wiped out of the community. If R0>1, the endemic equilibrium point is globally stable and the disease persists in the community. With transportation of infected pigs, the model only has the endemic equilibrium point which is locally stable. This indicates that with constant inflow of infected pigs the disease cannot be wiped out of the community

Modelling the role of treatment and vaccination in the control of transmission dynamics of pneumonia among children in Uganda

Paper presented at the 4th Strathmore International Mathematics Conference (SIMC 2017), 19 - 23 June 2017, Strathmore University, Nairobi, Kenya.Pneumonia is one of the leading causes of serious illness and deaths among children around the world. Efforts to effectively treat and control the spread of pneumonia is possible if its dynamics is well understood. In this paper, a mathematical model for the transmission dynamics of pneumonia is studied. The population is divided into five epidemiological classes to evaluate the role of treatment and vaccination in mitigating the spread of the disease. A system of differential equations is used to study the disease dynamics. Model analysis is carried out to establish the existence and stability of the steady states. It is revealed that the disease-free equilibrium point is globally stable if and only if the basic reproduction number R01, the endemic equilibrium point is globally stable and the disease persists at the endemic steady state. We infer the impact of control strategies on the dynamics of the disease through sensitivity analysis of the effective reproduction number Re from which the results showed that the combination of treatment and vaccination can eradicate the pneumonia infection

A Mathematical Model of Treatment and Vaccination Interventions of Pneumococcal Pneumonia Infection Dynamics

Streptococcus pneumoniae is one of the leading causes of serious morbidity and mortality worldwide, especially in young children and the elderly. In this study, a model of the spread and control of bacterial pneumonia under public health interventions that involve treatment and vaccination is formulated. It is found out that the model exhibits the disease-free and endemic equilibria. The disease-free equilibrium is stable if and only if the basic reproduction number R0<1 and the disease will be wiped out of the population. For R0≥1, the endemic equilibrium is globally stable and the disease persists. We infer the effect of these interventions on the dynamics of the pneumonia through sensitivity analysis on the effective reproduction number Re, from which it is revealed that treatment and vaccination interventions combined can eradicate pneumonia infection. Numerical simulation to illustrate the analytical results and establish the long term behavior of the disease is done. The impact of pneumonia infection control strategies is investigated. It is revealed that, with treatment and vaccination interventions combined, pneumonia can be wiped out. However, with treatment intervention alone, pneumonia persists in the population

Trapping the banana weevil, Cosmopolites sordidus, Germar: a mathematical perspective

Paper presented at the 5th Strathmore International Mathematics Conference (SIMC 2019), 12 - 16 August 2019, Strathmore University, Nairobi, KenyaA logistic equation incorporating trapping is formulated and parameterized to represent the population dynamics of the banana weevil, Cosmopolites Sordidus, (Germar). The steady states are obtained and their asymptotic stability established. The expression for the critical intrinsic growth rate is derived and its implications analyzed. The existence of possible bifurcations is investigated. It is found out that instability increases with the intrinsic growth rate and that as the intrinsic growth rate approaches the critical value, a mathematical catastrophe occurs at which the equilibria annihilate each other and coalesce into one. Numerical simulations are carried out to validate the results.Mbarara University of Science and Technology,Uganda. Bioversity International, Ugand

Threshold and stability results for a malaria model in a population with protective intervention among high‐risk groups

We develop a mathematical model for the dynamics of malaria with a varying population for which new individuals are recruited through immigration and births. In the model, we assume that non‐immune travellers move to endemic regions with sprays, smear themselves with jelly that is repellent to mosquitoes on arrival in malarious regions, others take long term antimalarials, and pregnant women and infants receive full treatment doses at intervals even when they are not sick from malaria (commonly referred to as intermittent preventive therapy). We introduce more features that describe the dynamics of the disease for the control strategies that protect the above vulnerable groups. The model analysis is done and equilibrium points are analyzed to establish their local and global stability. The threshold of the disease, the control reproduction number, is established for which the disease can be eliminated. First Published Online: 14 Oct 201