Papers by Abdullahi Mohammed Baba
World Scientific News, 2023
Despite official anti-corruption measures, Nigeria's chronic corruption is the country's greatest... more Despite official anti-corruption measures, Nigeria's chronic corruption is the country's greatest threat to stability, raising concerns about the country's institutions' ability to combat corruption. A model for the spread of corruption is developed and analyzed. The model's basic reproduction number, equilibriums, and stabilities are all taken into account. The Caputo fractional derivative operator of order is used to generate the model scheme of non-integer differential equations. The Laplace-Adomian Decomposition Method is used to estimate a solution to a set of non-integer differential equations. Numerical simulations are presented to demonstrate the method's dependability and simplicity.
In this paper, we proposed an ordinary differential equation model for the transmission of Hepati... more In this paper, we proposed an ordinary differential equation model for the transmission of Hepatitis B virus (BHV). The model accounted for the susceptible, exposed, infected, Chronic, and removed classes. We obtained the model's disease-free and endemic equilibrium points and the effective reproductive number. Further, from a thorough sensitivity analysis of the effective reproductive number, we extended the model by incorporating five time-dependent controls to cater to the vertical transmission, vaccination, testing, and treatment of acutely and chronically infected individuals. Numerical simulation was conducted to underscore the effects of the control in combating HBV.
14 March, 2023
In this paper, we formulated an optimal control model for the spread and control of human African... more In this paper, we formulated an optimal control model for the spread and control of human African Trypanosomiasis (HAT). Firstly, the ordinary differential equation model of HAT with basic properties and equilibrium states is presented. We used the method to obtain the all-important epidemiological threshold called the basic reproductive number. Three time-dependent controls representing personal protection, treatment and insecticide use were incorporated into the model using Pontryagin's principle. A numerical simulation was conducted to underscore the effects of optimal controls. The results show that the infective humans and tsetse flies have a downward trajectory with the three control strategies in place. In contrast, the susceptible humans and tsetse flies have an upward trajectory.
federal University Gusau, 2022
The disease that essentially affects the skin, the peripheral nerves, mucosal surfaces of the upp... more The disease that essentially affects the skin, the peripheral nerves, mucosal surfaces of the upper respiratory tract and the eyes. It is frequently surrounded by frightening, undesirable social stigmatization to them and their families and tales of leprosy patients being shunned as outcasts. In this paper, a deterministic mathematical model of the dynamics of disease is developed. The epidemic thresholds and equilibria for the model are determined and stabilities analyzed. Results from the analysis of the reproduction number propose that treatment will somehow contribute to a decrease in disease cases. This result recommends that, the control of the disease should lie more on treatment and public health education. Numerical simulations show the dynamics of the transmission of disease.
This paper considers a mathematical model for the spread of Plasmodium knowlesi malaria. The mode... more This paper considers a mathematical model for the spread of Plasmodium knowlesi malaria. The model incorporates recruitment of human, mosquito and macaque populations through a constant immigration, with a fraction of infective immigrants. The basic properties of model and equilibriums for the models are analyzed rigorously. The sensitivity analysis of the model is carried out to recognize the most sensitive parameters for the disease transmission. Thus, control strategy is presented and studied. Optimal control theory is applied to investigate optimal strategies for controlling the spread of the malaria using quarantine, insecticide spray and culling as the control variables. The results obtained from numerical simulation of the model show possible significant reduction of the disease spread using the combine control strategies.
AIP Conference Proceedings, 2015
The most significant and efficient measures against Plasmodium knowlesi outbreaks are efficient a... more The most significant and efficient measures against Plasmodium knowlesi outbreaks are efficient anti malaria drug, biological control in form of predatory mosquitoes and culling control strategies. In this paper optimal control theory is applied to a system of ordinary differential equation. It describes the disease transmission and Pontryagin’s Maximum Principle is applied for analysis of the control. To this end, three control strategies representing biological control, culling and treatment were incorporated into the disease transmission model. The simulation results show that the implementation of the combination strategy during the epidemic is the most cost-effective strategy for disease transmission.
AIP Conference Proceedings, 2015
Lassa virus that causes the Lassa fever is on the list of potential bio-weapons agents. It was re... more Lassa virus that causes the Lassa fever is on the list of potential bio-weapons agents. It was recently imported into Germany, the Netherlands, the United Kingdom and the United States as a consequence of the rapid growth of international traffic. A model with five mutually exclusive compartments related to Lassa fever is presented and the basic reproduction number analyzed. A sensitivity analysis of the deterministic model is performed. This is done in order to determine the relative importance of the model parameters to the disease transmission. The result of the sensitivity analysis shows that the most sensitive parameter is the human immigration, followed by human recovery rate, then person to person contact. This suggests that control strategies should target human immigration, effective drugs for treatment and education to reduced person to person contact.
Annual Research & Review in Biology, 2014
Malaria as among vector-borne diseases is reemerging in areas where control efforts were once eff... more Malaria as among vector-borne diseases is reemerging in areas where control efforts were once effective and emerging in areas though free of the disease as a consequence of human migration and rapid growth of international traffic from malaria prevalent areas of the world to malaria free zone. In this paper we develop a mathematical model for the spread of Plasmodium knowlesi malaria from infected humans to mosquitoes. The stability
A deterministic model for the transmission dynamics of Plasmodium Knowlesi malaria with direct tr... more A deterministic model for the transmission dynamics of Plasmodium Knowlesi malaria with direct transmission is developed. The model is analyzed using dynamical system techniques and it shows that the backward bifurcation occurs for some range of parameters. The model is extended to assess the impact of time dependent preventive (biological and chemical control) against the mosquitoes and vaccination for susceptible humans, while treatment for infected humans. The existence of optimal control is established analytically by the use of optimal control theory. Numerical simulations of the problem, suggest that applying the four control measure can effectively reduce if not eliminate the spread of Plasmodium Knowlesi in a community.
sciencepub.net
... [MA Liman, MO Ibrahim and MB Abdullahi. A Deterministic Mathematical Modeling Approach of Cho... more ... [MA Liman, MO Ibrahim and MB Abdullahi. A Deterministic Mathematical Modeling Approach of Cholera Transmission Analysis in Nigeria. Report and Opinion 2012; 4(1):44-47]. (ISSN: 1553-9873). ... Epidemics have never arisen from dead bodies. ...
British Journal of Mathematics & Computer Science, 2014
Aims: To investigate the optimal control strategy for Plasmodium knowlesi malaria in humans and m... more Aims: To investigate the optimal control strategy for Plasmodium knowlesi malaria in humans and macaques. Methodology: A Plasmodium knowlesi malaria model was developed using a deterministic system of differential equation and extended to include an optimal control of the disease. The optimal control model was analysis dynamically and numerically. Results: if the cost of biological control against the mosquito Larvae, the forest dwelling mosquitoes and chemical control against the adult mosquitoes is more than cost of treatment of the infected human, we observed that the control strategy yields increase in susceptible humans, decrease in the infected humans, infected macaques and mosquito population. This is one of the best strategies but treatment is very important for total elimination of Plasmodium knowlesi malaria in a community. Conclusion: Numerical simulations of the problem, suggest that applying the three control measure can effectively reduce if not eliminate the spread of Plasmodium knowlesi malaria in a community.
Applied Mathematical Sciences, 2013
We propose a new deterministic model for the dynamics of malaria and the effectiveness of drugs a... more We propose a new deterministic model for the dynamics of malaria and the effectiveness of drugs and the positivity of the model investigated. The human population was portioned into three distinct compartments of susceptible, infected and the recovered, while the mosquito population was portioned into two distinct Compartments of susceptible and the infected, giving rise to a set of five ordinary differential equations. A parameter ( A ) is introduced to measure the effectiveness of anti malarial drugs in the infected compartment. The dynamics of the model was obtained. It was observed that both the disease free equilibrium states will be stable if ( ) A > 60% and if the mosquitoes population is reduced the human population will also be stable. Numerical simulations were presented to show some results
PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES AND TECHNOLOGY 2020 (MATHTECH 2020): Sustainable Development of Mathematics & Mathematics in Sustainability Revolution
Rapid transmission of the novel coronavirus and its resulting condition has caught most countries... more Rapid transmission of the novel coronavirus and its resulting condition has caught most countries of the world off-guard. This work develops a fractional order model with seven compartments to describe the transmission and effects of control strategies of coronavirus. The Caputo fractional derivative operator of order (0,1) is applied to obtain the scheme of fractional differential equations (FDEs) of the model. The stability analysis is carried out and non-negative unique solution within the domain is verified. Laplace-Adomian Decomposition Method is applied to work out an approximate solution of the FDEs. The solution of the FDEs in the form of infinite series is obtained. The obtained results are compared with the differential transform method case, which converges rapidly to its exact value. Numerical simulations are presented to show the reliability and simplicity of the method.
This study discusses the Stability of equilibrium states of a model in an attempt to suggest cont... more This study discusses the Stability of equilibrium states of a model in an attempt to suggest control of and Eradication strategies for malaria in a community. The model exhibits two equilibria namely; the trivial equilibrium state and diseases free equilibrium state. The Model analysis shows that combination of both treatment and preventive method can eradicate malaria cases.(Abdullahi Mohammed Baba: A Mathematical Model for Assessing the Control of and Eradication strategies for Malaria in a Community. (ABDULLAHI MOHAMMED BABA. A Mathematical Model for Assessing the Control of and Eradication strategies for Malaria in a Community. Report and Opinion 2012;4(2):7-12). (ISSN: 1553-9873). http://www.sciencepub.net/report . 2
Model to forecast malaria outbreaks Phys. Today Abstract. The most significant and efficient meas... more Model to forecast malaria outbreaks Phys. Today Abstract. The most significant and efficient measures against Plasmodium knowlesi outbreaks are efficient anti malaria drug, biological control in form of predatory mosquitoes and culling control strategies. In this paper optimal control theory is applied to a system of ordinary differential equation. It describes the disease transmission and Pontryagin's Maximum Principle is applied for analysis of the control. To this end, three control strategies representing biological control, culling and treatment were incorporated into the disease transmission model. The simulation results show that the implementation of the combination strategy during the epidemic is the most cost-effective strategy for disease transmission.
A mathematical model for the transmission dynamics of Knowlesi malaria is developed. The model, w... more A mathematical model for the transmission dynamics of Knowlesi malaria is developed. The model, which consists of 8 ordinary differential equations, is analyzed rigorously. The Knowlesi malaria model was extended to incorporate the effect of seasonality in the transmission rates of knowlesi malaria; the seasonal forcing basic reproduction number is investigated analytically. The sensitivity analysis of the basic reproduction number of the sensuality is investigated. Numerical analysis is carried out considering different strength of seasonality to determine the effect of seasonal biting rates on the susceptible humans, mosquitoes and macaques.
This paper considers a mathematical model for the spread of Plasmodium knowlesi malaria. The mode... more This paper considers a mathematical model for the spread of Plasmodium knowlesi malaria. The model incorporates recruitment of human, mosquito and macaque populations through a constant immigration, with a fraction of infective immigrants. The basic properties of model and equilibriums for the models are analyzed rigorously. The sensitivity analysis of the model is carried out to recognize the most sensitive parameters for the disease transmission. Thus, control strategy is presented and studied. Optimal control theory is applied to investigate optimal strategies for controlling the spread of the malaria using quarantine, insecticide spray and culling as the control variables. The results obtained from numerical simulation of the model show possible significant reduction of the disease spread using the combine control strategies.
Lassa virus that causes the Lassa fever is on the list of potential bio-weapons agents. It was re... more Lassa virus that causes the Lassa fever is on the list of potential bio-weapons agents. It was recently imported
into Germany, the Netherlands, the United Kingdom and the United States as a consequence of the rapid growth of
international traffic. A model with five mutually exclusive compartments related to Lassa fever is presented and the basic
reproduction number analyzed. A sensitivity analysis of the deterministic model is performed. This is done in order to
determine the relative importance of the model parameters to the disease transmission. The result of the sensitivity
analysis shows that the most sensitive parameter is the human immigration, followed by human recovery rate, then person
to person contact. This suggests that control strategies should target human immigration, effective drugs for treatment and
education to reduced person to person contact.
Lassa virus that causes the Lassa fever is on the list of potential bio-weapons agents. It was re... more Lassa virus that causes the Lassa fever is on the list of potential bio-weapons agents. It was recently imported
into Germany, the Netherlands, the United Kingdom and the United States as a consequence of the rapid growth of
international traffic. A model with five mutually exclusive compartments related to Lassa fever is presented and the basic
reproduction number analyzed. A sensitivity analysis of the deterministic model is performed. This is done in order to
determine the relative importance of the model parameters to the disease transmission. The result of the sensitivity
analysis shows that the most sensitive parameter is the human immigration, followed by human recovery rate, then person
to person contact. This suggests that control strategies should target human immigration, effective drugs for treatment and
education to reduced person to person contact.
Malaria as among vector-borne diseases is reemerging in areas where control efforts were once eff... more Malaria as among vector-borne diseases is reemerging in areas where control efforts were once effective and emerging in areas though free of the disease as a consequence of human migration and rapid growth of international traffic from malaria prevalent areas of the world to malaria free zone. In this paper we develop a mathematical model for the spread of Plasmodium knowlesi malaria from infected humans to mosquitoes. The stability 4483 analysis of the model is investigated rigorously. The model is extended to assess the impact of time dependent preventive (biological and chemical control) against the mosquitoes and treatment for infected humans. The existence of optimal control is established analytically by the use of optimal control theory. Numerical simulations of the problem, suggest that applying the three control measure can effectively reduce if not eliminate the spread of Plasmodium knowlesi malaria in a community.
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Papers by Abdullahi Mohammed Baba
into Germany, the Netherlands, the United Kingdom and the United States as a consequence of the rapid growth of
international traffic. A model with five mutually exclusive compartments related to Lassa fever is presented and the basic
reproduction number analyzed. A sensitivity analysis of the deterministic model is performed. This is done in order to
determine the relative importance of the model parameters to the disease transmission. The result of the sensitivity
analysis shows that the most sensitive parameter is the human immigration, followed by human recovery rate, then person
to person contact. This suggests that control strategies should target human immigration, effective drugs for treatment and
education to reduced person to person contact.
into Germany, the Netherlands, the United Kingdom and the United States as a consequence of the rapid growth of
international traffic. A model with five mutually exclusive compartments related to Lassa fever is presented and the basic
reproduction number analyzed. A sensitivity analysis of the deterministic model is performed. This is done in order to
determine the relative importance of the model parameters to the disease transmission. The result of the sensitivity
analysis shows that the most sensitive parameter is the human immigration, followed by human recovery rate, then person
to person contact. This suggests that control strategies should target human immigration, effective drugs for treatment and
education to reduced person to person contact.
into Germany, the Netherlands, the United Kingdom and the United States as a consequence of the rapid growth of
international traffic. A model with five mutually exclusive compartments related to Lassa fever is presented and the basic
reproduction number analyzed. A sensitivity analysis of the deterministic model is performed. This is done in order to
determine the relative importance of the model parameters to the disease transmission. The result of the sensitivity
analysis shows that the most sensitive parameter is the human immigration, followed by human recovery rate, then person
to person contact. This suggests that control strategies should target human immigration, effective drugs for treatment and
education to reduced person to person contact.
into Germany, the Netherlands, the United Kingdom and the United States as a consequence of the rapid growth of
international traffic. A model with five mutually exclusive compartments related to Lassa fever is presented and the basic
reproduction number analyzed. A sensitivity analysis of the deterministic model is performed. This is done in order to
determine the relative importance of the model parameters to the disease transmission. The result of the sensitivity
analysis shows that the most sensitive parameter is the human immigration, followed by human recovery rate, then person
to person contact. This suggests that control strategies should target human immigration, effective drugs for treatment and
education to reduced person to person contact.