Schistosomiasis is a neglected disease affecting almost every region of the world, with its endem... more Schistosomiasis is a neglected disease affecting almost every region of the world, with its endemicity mainly experience in sub-Saharan Africa. It remains difficult to eradicate due to heterogeneity associated with its transmission mode. A mathematical model of Schistosomiasis integrating heterogeneous host transmission pathways is thus formulated and analyzed to investigate the impact of the disease in the human population. Mathematical analyses are presented, including establishing the existence and uniqueness of solutions, computation of the model equilibria, and the basic reproduction number (R0). Stability analyses of the model equilibrium states show that disease-free and endemic equilibrium points are locally and globally asymptotically stable whenever R0 < 1 and R0>1, respectively. Additionally, bifurcation analysis is carried out to establish the existence of a forward bifurcation around R0 = 1. Using Latin-hypercube sampling, global sensitivity analysis was performed...
This study presents a deterministic model for the environmental transmission dynamics of monkeypo... more This study presents a deterministic model for the environmental transmission dynamics of monkeypox (MPX) in the presence of quarantine and vaccination. The analysis of the model established three important equilibrium states namely; monkeypox-free equilibrium (MPXV-FE), infected rodent-free endemic equilibrium (IRF-EE), and coexistence equilibrium (CO-EE). The local and global stability of the equilibrium states is examined in terms of reproduction numbers. For global stability, the comparison theory is used for MPXV-FE while the Voltera-Lyapunov matrix theory is used for IRF-EE. Sensitivity analysis is performed using the Latin hypercube sampling method, and the results showed that environmental transmission parameters are the main driver of infection in the dynamics of MPX infection. This is further supported by numerical simulations to show the impact of environmental transmission on the MPX infection and also the validity of the theoretical analysis. Based on the results, it is ...
In this paper, a mathematical model for Lassa fever transmission dynamics with rodent logistic gr... more In this paper, a mathematical model for Lassa fever transmission dynamics with rodent logistic growth is developed and analysed. The stability analysis of the autonomous system of the model is presented. The sensitivity analysis of the parameters is performed using the Partial Rank Correlation Coefficient (PRCC) technique. The non-autonomous model is further analysed for stability of disease-free periodic equilibrium(DFPE) in terms of reproduction number ratio, $R_{0t}.$ It shown that DFPE is locally asymptotically stable when $R_{0t}<1$ and unstable if $R_{0t}>1$. Additionally, the optimal control model is formulated with five control measures namely; personal protective equipment and avoiding hunting of rodents, proper handling of food, treatment and isolation, cleaning and disinfecting the environment, and rodent control. Simulations of the optimal control model show that the combined implementation of the five control measures reduce Lassa fever spread in the population. H...
The recent outbreak of the novel coronavirus (COVID-19) pandemic which originated from the Wuhan ... more The recent outbreak of the novel coronavirus (COVID-19) pandemic which originated from the Wuhan City of China has devastated many parts of the globe. At present, non-pharmaceutical interventions are the widely available measures being used in combating and controlling this disease. There is great concern over the rampant unaccounted cases of individuals skipping the border during this critical period in time. We develop a deterministic compartmental model to investigate the impact of escapees on the transmission dynamics of COVID-19 in Zimbabwe. A suitable Lyapunov function has been used to show that the disease-free equilibrium is globally asymptotically stable provided ℛ0< 1. We performed global sensitivity analysis using the Latin-hyper cube sampling method and partial rank correlation coefficients to determine the most influential model parameters on the short and long term dynamics of the pandemic, so as to minimize uncertainties associated with our variables and parameters...
Summary in EnglishHIV/AIDS continues to be a huge global burden having claimed million lives worl... more Summary in EnglishHIV/AIDS continues to be a huge global burden having claimed million lives worldwide. It targets the immune system and defence mechanisms against infections such as the human pa- pillomavirus(HPV). HPV can be classifi ed as low-risk or high-risk, with high-risk types (16 and 18) mainly being responsible for cancers, such as cervical cancer in women. HPV is a very common sexually transmitted infection that is given less attention, with many men and women living and spreading infection through unsafe sexual practices. In this thesis we present a mathematical model for the transmission dynamics of HPV in-host in the presence of immune response represented by Cytotoxic T-Lymphocytes cells (CTL). The model presented considers the effects of latent HPV infections and the model dynamics are effectively analysed. The model presents two important reproduction numbers, that is the basic reproduction number R0 and the CTL reproduction number RK. The simulation dynamics of the...
We consider a model with mass testing and isolation mimicking the current policies implemented in... more We consider a model with mass testing and isolation mimicking the current policies implemented in Nigeria and use the Nigerian daily cumulative cases to calibrate the model to obtain the optimal mass testing and isolation levels. Mathematical analysis was done and important thresholds such the peak size relation and final size relation were obtained. Global stability analysis of the disease-free equilibrium indicated that COVID-19 can be eradicated provided that and unstable otherwise. Results from simulations revealed that an increase in mass testing and reduction of transmission from isolated individuals are associated with benefits of increasing detected cases, lowering peaks of symptomatic cases, increase in self-isolating cases, decrease in cumulative deaths and decrease in admissions into monitored isolation facilities in the case of Nigeria.
Recently, due to the global increase in new cases of infections, the World Health Organisation de... more Recently, due to the global increase in new cases of infections, the World Health Organisation declared COVID-19 disease a pandemic. We present a deterministic model to investigate the impact of de...
Schistosomiasis is a neglected disease affecting almost every region of the world, with its endem... more Schistosomiasis is a neglected disease affecting almost every region of the world, with its endemicity mainly experience in sub-Saharan Africa. It remains difficult to eradicate due to heterogeneity associated with its transmission mode. A mathematical model of Schistosomiasis integrating heterogeneous host transmission pathways is thus formulated and analyzed to investigate the impact of the disease in the human population. Mathematical analyses are presented, including establishing the existence and uniqueness of solutions, computation of the model equilibria, and the basic reproduction number (R0). Stability analyses of the model equilibrium states show that disease-free and endemic equilibrium points are locally and globally asymptotically stable whenever R0 < 1 and R0>1, respectively. Additionally, bifurcation analysis is carried out to establish the existence of a forward bifurcation around R0 = 1. Using Latin-hypercube sampling, global sensitivity analysis was performed...
This study presents a deterministic model for the environmental transmission dynamics of monkeypo... more This study presents a deterministic model for the environmental transmission dynamics of monkeypox (MPX) in the presence of quarantine and vaccination. The analysis of the model established three important equilibrium states namely; monkeypox-free equilibrium (MPXV-FE), infected rodent-free endemic equilibrium (IRF-EE), and coexistence equilibrium (CO-EE). The local and global stability of the equilibrium states is examined in terms of reproduction numbers. For global stability, the comparison theory is used for MPXV-FE while the Voltera-Lyapunov matrix theory is used for IRF-EE. Sensitivity analysis is performed using the Latin hypercube sampling method, and the results showed that environmental transmission parameters are the main driver of infection in the dynamics of MPX infection. This is further supported by numerical simulations to show the impact of environmental transmission on the MPX infection and also the validity of the theoretical analysis. Based on the results, it is ...
In this paper, a mathematical model for Lassa fever transmission dynamics with rodent logistic gr... more In this paper, a mathematical model for Lassa fever transmission dynamics with rodent logistic growth is developed and analysed. The stability analysis of the autonomous system of the model is presented. The sensitivity analysis of the parameters is performed using the Partial Rank Correlation Coefficient (PRCC) technique. The non-autonomous model is further analysed for stability of disease-free periodic equilibrium(DFPE) in terms of reproduction number ratio, $R_{0t}.$ It shown that DFPE is locally asymptotically stable when $R_{0t}<1$ and unstable if $R_{0t}>1$. Additionally, the optimal control model is formulated with five control measures namely; personal protective equipment and avoiding hunting of rodents, proper handling of food, treatment and isolation, cleaning and disinfecting the environment, and rodent control. Simulations of the optimal control model show that the combined implementation of the five control measures reduce Lassa fever spread in the population. H...
The recent outbreak of the novel coronavirus (COVID-19) pandemic which originated from the Wuhan ... more The recent outbreak of the novel coronavirus (COVID-19) pandemic which originated from the Wuhan City of China has devastated many parts of the globe. At present, non-pharmaceutical interventions are the widely available measures being used in combating and controlling this disease. There is great concern over the rampant unaccounted cases of individuals skipping the border during this critical period in time. We develop a deterministic compartmental model to investigate the impact of escapees on the transmission dynamics of COVID-19 in Zimbabwe. A suitable Lyapunov function has been used to show that the disease-free equilibrium is globally asymptotically stable provided ℛ0< 1. We performed global sensitivity analysis using the Latin-hyper cube sampling method and partial rank correlation coefficients to determine the most influential model parameters on the short and long term dynamics of the pandemic, so as to minimize uncertainties associated with our variables and parameters...
Summary in EnglishHIV/AIDS continues to be a huge global burden having claimed million lives worl... more Summary in EnglishHIV/AIDS continues to be a huge global burden having claimed million lives worldwide. It targets the immune system and defence mechanisms against infections such as the human pa- pillomavirus(HPV). HPV can be classifi ed as low-risk or high-risk, with high-risk types (16 and 18) mainly being responsible for cancers, such as cervical cancer in women. HPV is a very common sexually transmitted infection that is given less attention, with many men and women living and spreading infection through unsafe sexual practices. In this thesis we present a mathematical model for the transmission dynamics of HPV in-host in the presence of immune response represented by Cytotoxic T-Lymphocytes cells (CTL). The model presented considers the effects of latent HPV infections and the model dynamics are effectively analysed. The model presents two important reproduction numbers, that is the basic reproduction number R0 and the CTL reproduction number RK. The simulation dynamics of the...
We consider a model with mass testing and isolation mimicking the current policies implemented in... more We consider a model with mass testing and isolation mimicking the current policies implemented in Nigeria and use the Nigerian daily cumulative cases to calibrate the model to obtain the optimal mass testing and isolation levels. Mathematical analysis was done and important thresholds such the peak size relation and final size relation were obtained. Global stability analysis of the disease-free equilibrium indicated that COVID-19 can be eradicated provided that and unstable otherwise. Results from simulations revealed that an increase in mass testing and reduction of transmission from isolated individuals are associated with benefits of increasing detected cases, lowering peaks of symptomatic cases, increase in self-isolating cases, decrease in cumulative deaths and decrease in admissions into monitored isolation facilities in the case of Nigeria.
Recently, due to the global increase in new cases of infections, the World Health Organisation de... more Recently, due to the global increase in new cases of infections, the World Health Organisation declared COVID-19 disease a pandemic. We present a deterministic model to investigate the impact of de...
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