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Ebola Virus disease (EVD) is an emerging and re-emerging zoonotic disease which mostly occur in Africa. Both prediction of the next EVD and controlling an ongoing outbreak remain challenging to disease prone countries. Depending on previous experiences to curb an outbreak is subjective and often inadequate as temporal socioeconomic advances are dynamic and complex at each disease. We hypothesize that a scientific model would predict EVD disease outbreak control. In this work, a mathematical model with a convex incidence rate for an optimal control model of Ebola Virus Disease is formulated and analyzed. An optimal control strategy which aims at reducing the number of infected individuals in the population and increasing the number of recovered through treatment is evaluated. Three control measures: tracing of contacts, lock-down and treatment have been considered. A qualitative analysis and numerical experiments are performed on the model and the findings reveal that the most expensive strategy involved imposing lock-down and contact tracing of the infected while the cheapest alternative was lock-down and treatment of the infected. Hence, policy makers should concentrate on treatment and lock down to combat the disease.

Measles is a highly contagious airborne disease that is endemic in many developing countries with low levels of vaccination coverage. In this paper, we propose a deterministic compartmental mathematical model for measles disease dynamics. We establish the global stability conditions for the disease-free and endemic equilibria using the Lyapunov function stability method. \textcolor{red}{Using arbitrary parameters it is obtained that the proposed model exhibits forward bifurcation}. Numerical integration using MATLAB software was used to simulate the model solution of the forward problem. We calibrate the proposed model to estimate the parameters with a 95\% confidence interval (CI) using real data from Ethiopia by formulating an inverse problem. We notice that the model fits well with the real data of Ethiopia. The estimated basic reproduction number ($R_0$) is found to be $R_0=1.3973$ which proves that the disease is endemic. It is also obtained from the local sensitivity analysis that reducing the transmission rate and increasing the vaccination rate could effectively minimize the $R_0$.

There is a growing interest in using mathematical models to understand crime dynamics, crime prevention, and detection. The past decade has experienced a relative reduction in conventional crimes, but this has been replaced by significant increases in cybercrime. We use a system of nonlinear differential equations to explore the impact of criminal location in relation to cyber networks on the amount of cybercrime. Using steady-state analysis and extensive numerical simulations, we find that the location of criminals relative to the network does not impact the system qualitatively although there are quantitative differences. Cyber networks that are more clustered are likely to experience greater levels of cybercrime but there is also a saturation effect that limits the level of victimisation as the number of criminals attempting to undertake crimes on a given network increases.

A deterministic model was formulated and employed in the analysis of the dynamics of tuberculosis with a keen emphasis on vaccination and drug resistance as the first line of treatment. It was assumed that some of the susceptible population were vaccinated but with temporal immunity. This is due to the fact that vaccines do not confer permanent immunity. Moreover, part of the infected individual after treatment grows resistance to the drug. Infective immigrants were also considered to be part of the population. The basic reproductive number for the model is estimated using the next-generation matrix method. The equilibrium points of the TB model and their local and global stability were determined. It was established that if the basic reproductive number was less than unity R 0 < 1 , then the disease free equilibrium is stable and unstable if R 0 > 1 . Furthermore, we investigated the optimal prevention, treatment, and vaccination as control measures for the disease. As the objective functional was optimised, there have been a significant reduction in the number of infections and an increase in the number of recovery. The best control measure in combating tuberculosis infections is prevention and vaccination of the susceptible population.

Campylobacter genus is the bacteria responsible for campylobacteriosis infections, and it is the commonest cause of gastroenteritis in adults and infants. The disease is hyperendemic in children in most parts of developing countries. It is a zoonotic disease that can be contracted via direct contact, food, and water. In this paper, we formulated a deterministic model for Campylobacteriosis as a zoonotic disease with optimal control and to determine the best control measure. The nonstandard finite difference scheme was used for the model analysis. The disease-free equilibrium of the scheme in its explicit form was determined, and it was shown to be both locally and globally asymptotically stable. The campylobacteriosis model was extended to optimal control using prevention of susceptible humans contracting the disease and treatment of infected humans and animals. The objective function was optimised, and it was established that combining prevention of susceptible humans and treatment of infected animals was the effective control measure in combating campylobacteriosis infections. An analysis of the effects of contact between susceptible and infected animals as well susceptible and infected humans was conducted. It showed an increase in infected animals and humans whenever the contact rate increases and decreases otherwise. Biologically, it implies that campylobacteriosis infections can be controlled by ensuring that interactions among susceptible humans, infected animals, and infected humans is reduced to the barest minimum.

Listeriosis is a serious disease caused by the germ Listeria monocytogenes. People usually become ill with listeriosis after eating contaminated food including meat. The disease primarily affects pregnant women, newborns, older adults, and people with weakened immune systems. In this paper, we propose and scrutinize a model problem describing the transmission dynamics of Listeriosis epidemic in animal and human population using the stability theory of differential equations. The model is qualitatively analysed for the basic reproduction number as well as possibility of forward and backward bifurcation with respect to the stability of disease free and endemic equilibria. The impact of the model parameters on the disease was evaluated via sensitivity analysis. An extension of the model to include time dependent control variables such as treatment, vaccination and education of susceptible (human) is carried out. Using Pontryagin’s Maximum Principle, we obtain the optimal control strategies needed for combating Listeriosis disease. Numerical simulation of the model is performed and pertinent results are displayed graphically and discussed quantitatively.

Listeriosis is an illness caused by the germ Listeria monocytogenes. Generally, humans are infected with listeriosis after eating contaminated food. Listeriosis mostly affects people with weakened immune systems, pregnant women and newborns. In this paper, a model describing the dynamics of Listeriosis is developed and analysed using ordinary differential equations. The model was analysed both quantitatively and qualitatively for its local and global stability, basic reproductive number and parameter contributions to the basic reproductive number to understand the impact of each parameter on the disease spread. The Listeriosis model has been extended to include time dependent control variables such as treatment of both humans and animals, vaccination and education of humans. Pontryagin’s Maximum Principle was introduced to obtain the best optimal control strategies required for curbing Listeriosis infections. Numerical simulation was performed and the results displayed graphically and discussed. Cost effectiveness analysis was conducted using the intervention averted ratio (IAR) concepts and it was revealed that the most effective intervention strategy is the treatment of infected humans and animals.

Anthrax is an infection caused by bacteria and it affects both human and animal populations. The disease can be categorized under zoonotic diseases and humans can contract infections through contact with infected animals, ingest contaminated dairy and animal products. In this paper, we developed a mathematical model for anthrax transmission dynamics in both human and animal populations with optimal control. The qualitative solution of the model behaviour was analyzed by determining Rhv, equilibrium points and sensitivity analysis. A vaccination class was incorporated into the model with waning immunity. Local and global stability of the model’s equilibria was found to be locally asymptotically stable whenever Rhv Rhv. It was revealed that reducing animal and human interaction rate, would decrease Rhv. We extended the model to optimal control in order to find the best control strategy in reducing anthrax infections. It showed that the effective strategy in combating the anthrax epidemics is vaccination of animals and prevention of humans.

A deterministic mathematical model of typhoid fever incorporating unprotected humans is formulated in this study and employed to study local and global stability of equilibrium points. The model incorporating Susceptible, unprotected, Infectious and Recovered humans which are analyzed mathematically and also result into a system of ordinary differential equations which are used for interpretations and comparison to the qualitative solutions in studying the spread dynamics of typhoid fever. Jacobian matrix was considered in the study of local stability of disease free equilibrium point and Castillo-Chavez approach used to determine global stability of disease free equilibrium point. Lyapunov function was used to study global stability of endemic equilibrium point. Both equilibrium points (DFE and EE) were found to be local and globally asymptotically stable. This means that the disease will be dependent on numbers of unprotected humans and other factors who contributes positively to the transmission dynamics.

In this paper, we employed a deterministic model in the analysis of the dynamics of Tuberculosis with a keen interest in vaccination and drug resistance as the first line of treatment. It was assumed that some of the susceptible population were vaccinated but with temporal immunity. This is due to the fact that vaccines do not confer permanent immunity. Moreover, Part of the infected individual after treatment grow resistance to the drug. Infective immigrants were also considered to be part of the population. The basic reproductive number for the model is estimated using the Next Generation Matrix method. The equilibrium points of the TB model and their local and global stability were determined. It was established that if the basic reproductive number was less than unity (R 0 1. Furthermore, we investigated the optimal prevention, treatment and vaccination as control measures for the disease. It was established that the best control measure in combating Tuberculosis infections is prevention and vaccination of susceptible population.

Tuberculosis (TB) is a major public health concern in many developing countries. Mycobacterium tuberculosis is a major cause of morbidity and mortality in Africa. Tuberculosis infection is curable but in the cases of incomplete treatment, the remains of Mycobacterium tuberculosis in the human body usually results in the bacterium developing resistant to antibiotics. In this study we developed a model that explains the dynamics of tuberculosis infection in the presence of drug resistance. The basic reproduction number of the model was computed using the next generation matrix approach. The disease free equilibrium and endemic equilibrium were obtained and their stability analysis were carried out. It revealed that they were locally and globally asymptotically stable whenever the reproductive number was less than unity. Numerical simulation of the TB model was conducted and the result revealed that contact rate can reduce or eliminate the sensitive strain and reduce drug resistant of tuberculosis.

Limited resources hinder the control and prevention of hepatitis B in some communities in Ghana and the Brong Ahafo region is no different. In this paper, we formulated a model that explains the spread of hepatitis B and suggested an intervention to minimise its effect. We analysed the local and global stability of the disease as well as the basic reproduction number. It was established that the disease is locally asymptotically stable whenever the basic reproduction number is less than unity and unstable otherwise. Optimal control theory was incorporated to determine the best control strategy in combating the spread of hepatitis B in the environment. The following control strategies were employed; treatment, vaccination and prevention. The results of the numerical simulation showed that the best optimal control strategy in combating the spread of the infection was vaccination of susceptible and treatment of the infected population.

In this paper, a deterministic model for the co-dynamics of Anthrax and Listerios diseases was formulated to investigate the qualitative and quantitative relationship of both diseases by incorporating prevention and treatment controls. The basic reproduction number, stability, existence and equilibria of each disease was investigated separately. The Anthrax-Listeriosis co-dynamics model was analysed and it the idea of backward bifurcation existed. The impact of Anthrax infection on the transmission of Listeriosis was determined. The Anthrax-Listeriosis co-dynamics model was extended and included time dependent control variables. Pontryagin’s Maximum Principle was used to obtain the optimal control strategies needed for eradication of Anthrax-Listeriosis infections. We performed the numerical simulation of the co-dynamics model in order to give the quantitative implications of the results. It was established that Anthrax infection can be attributed to increased risk of Listeriosis but Listeriosis infection is not associate with the risk of Anthrax. Effective control of Anthrax means incorporating both the intervention srategies of Anthrax and Listeriosis.

The recent development of making secondary school education free in Ghana has raised concerns about the level of preparedness of teachers to teach students with diverse needs in one classroom. Sign...