The long and binding treatment of tuberculosis (TB) at least 6-8 months for the new cases, the partial immunity given by BCG vaccine, the loss of immunity after a few years doing that strategy of TB control via vaccination and treatment of infectious are not sufficient to eradicate TB. TB is an infectious disease caused by the bacillus Mycobacterium tuberculosis. Adults are principally attacked. In this work, we assess the impact of vaccination in the spread of TB via a deterministic epidemic model (SV ELI) (Susceptible, Vaccinated, Early latent, Late latent, Infectious). Using the Lyapunov-Lasalle method, we analyse the stability of epidemic system (SV ELI) around the equilibriums (disease-free and endemic). The global asymptotic stability of the unique endemic equilibrium whenever R 0 > 1 is proved, where R 0 is the reproduction number. We prove also that when R 0 is less than 1, TB can be eradicated. Numerical simulations, using some TB data found in the literature in relation with Cameroon, are conducted to approve analytic results, and to show that vaccination coverage is not sufficient to control TB, effective contact rate has a high impact in the spread of TB.

In this paper, we derive and analyse a model for the control of arboviral diseases which takes into account an imperfect vaccine combined with some other control measures already studied in the literature. We begin by analysing the basic model without control. We prove the existence of two disease-free equilibrium points and the possible existence of up to two endemic equilibrium points (where the disease persists in the population). We show the existence of a transcritical bifurcation and a possible saddle-node bifurcation and explicitly derive threshold conditions for both, including defining the basic reproduction number, [Formula: see text], which provides whether the disease can persist in the population or not. The epidemiological consequence of saddle-node bifurcation is that the classical requirement of having the reproduction number less than unity, while necessary, is no longer sufficient for disease elimination from the population. It is further shown that in the absence of disease-induced death, the model does not exhibit this phenomenon. The model is extended by reformulating the model as an optimal control problem, with the use of five time dependent controls, to assess the impact of vaccination combined with treatment, individual protection and two vector control strategies (killing adult vectors and reduction of eggs and larvae). By using optimal control theory, we establish conditions under which the spread of disease can be stopped, and we examine the impact of combined control tools on the transmission dynamic of disease. The Pontryagin's maximum principle is used to characterize the optimal control. Numerical simulations and efficiency analysis show that, vaccination combined with other control mechanisms, would reduce the spread of the disease appreciably.

The lack of treatment for poliomyelitis doing that only means of preventing is immunization with live oral polio vaccine (OPV) or/and inactivated polio vaccine (IPV). Poliomyelitis is a very contagious viral infection caused by poliovirus. Children are principally attacked. In this paper, we assess the impact of vaccination in the control of spread of poliomyelitis via a deterministic SVEIR (Susceptible-VaccinatedLatent-Infectious-Removed) model of infectious disease transmission, where vaccinated individuals are also susceptible, although to a lesser degree. Using LyapunovLasalle methods, we prove the global asymptotic stability of the unique endemic equilibrium whenever vac 1 >  . Numerical simulations, using poliomyelitis data from Cameroon, are conducted to approve analytic results and to show the importance of vaccinate coverage in the control of disease spread.

COVID-19 is an acute respiratory illness in humans caused by a coronavirus, capable of producing severe symptoms and, in some cases, death, especially in older people and those with underlying health conditions. It was originally identified in China in 2019 and became a pandemic in 2020. On 6 March 2020, Cameroon recorded its first cases of infection with COVID-19. The Government of Cameroon (GOC) took 13 barrier measures on 18 March 2020. On 1 May 2020, 19 new measures were adopted, easing restrictions and encouraging economic activity. On 1 June, schools and universities were reopened, after which massive screening began to take place throughout the country. In this study, we have modelled the COVID-19 epidemic in Cameroon in order to assess the governmental measures of response and predict the behaviour of epidemic As a result of these measures, the pandemic evolved in three phases. The first phase began on 18 March and ended on 15 May 2020. During this phase, the actual curve of cumulative positive cases based on field data closely fit the theoretical curve resulting from mathematical modelling. In the beginning of May, we predicted that nearly 3000 positive cases would be declared by mid-May 2020. The actual data confirmed these predictions: there were 2954 cases as of 15 May 2020. The second phase, beyond mid-May 2020, encompasses the period when the GOC’s relaxation of measures takes effect. This phase was marked by an acceleration of the cumulative number of positive cases starting in the third week of May, postponing the expected peak by two weeks. Under Phase 2 conditions, the onset of the peak will occur in early June and extend through the first two weeks of June. However, a third phase occurs in the first week of June, with the reopening of schools and universities combined with massive screening; the peak is therefore expected in the second week of June (around 15 June). The GOC should, at this stage, strengthen its response plan by tripling the current coverage capacity to regain the first phase convergence conditions associated with the first 13 measures. The pandemic will begin its descent in the month of august, but COVID-19 will remain endemic for at least one year.