Lassa fever is an acute viral hemorrhage fever cause by the Lassa virus, a member of the Arenaviridae family. Direct contact with biofluids or breaches in the skin of infected individuals can also transmit Lassa fever. West African nations, in particular, Nigeria face significant health concerns, with 100,000-300,000 infections and annual death of 5,000 [1-3]. According to WHO research, "Lassa fever is endemic in Nigeria and has its peak period during the dry seasons because Mastomys rat reproduces more in the wet season" WHO [4]. Lassa fever has an incubation period typically lasts 5-21 days after the patient comes into contact with the virus. Approximately 80% of Lassa fever virus infections result in mild symptoms, such as a slight fever, general weakness, and a headache. However, in 20% of infected people, the disease progresses to more serious symptoms, including hemorrhage (bleeding), respiratory difficulty, frequent vomiting, face swelling, discomfort in the chest, back, and abdomen, and shock, as well as neurological problems such as hearing loss and tremors [5-6]. Virus levels in the blood are known to peak between four and nine days following the latency period [7]. The overall case fatality rate (CFR) is 1%, but it might reach 15% or more for patients hospitalized with a severe presentation WHO [3]. In severe or fatal instances, mortality occurs within two weeks of the onset of illness symptoms [3,8]. Lassa fever is generally treated with the antiviral drug ribavirin, which has been very effective when given early in the course of the disease.
As a result, implementing an effective control program is critical to estimating not only the influence on the reduction of confirmed cases, severe cases, and deaths, but also the economic damages caused [9].
Various mathematical models have been developed to investigate and capture physical, biological, chemical, economical and many complexes real world problems. Numerous studies have applied mathematical models to epidemiology, particularly focusing on the transmission dynamics and of infectious diseases see for instance [10-14,36-40]. However, Lassa fever disease in particular have been given limited attention, resulting in little or few information’s regarding its transmission dynamics. Some studies attempted to study Lassa virus dynamics using mathematical modelling approach. For instance, Okolo [15] explored the dynamics transmission of Lassa fever with control measures, incorp susceptible, latent, Asymptomatic Infection Symptomatic infection and recovered human populations alongside infected Susceptible and infected rats respectively. Their findings highlighted that transmission parameters are the major Couse of the disease, suggesting that combining isolation procedures with effective treatment of the human plays a significant role in controlling the disease. Ojo [16] examined dynamic of Lassa fever in Nigeria, concluding that any control strategy capable of reducing the rodent population and risks of transmission could help in mitigating the disease. Guofo [17] further analyzed Lassa fever dynamics using mathematical modeling together with combining control parameters led to marked decrease of the total infected population. Ibrahim [18] studied the sensitivity analysis with relapse and re-infections scenarios, unveiling that recovered humans could become susceptible again with relapse, re-infection and treatment rate on the affected population. Musa [9] examined the similarities of the transmission of Lassa fever in the three most endemic areas and suggested that recruitment of the susceptible individuals, lead to increase in their sub-population, contributes significantly to increase in the infection. Mc Kendrick [14] studied the seasonality of Lassa fever outbreaks, revealing that there is an increase outbreak during the peak of the dry season and suggested that combating this menace, there is the need of controlling the reservoir of the rodent during this period. Abdulhamid [19] analyzed the effects of environmental transmission, identifying the most sensitive parameters and demonstrating the burden of pathogens in the transmission process. Bakare [2], proposed a compartmental model the transmission dynamics of Lassa fever, suggesting that combination of multiple interventions is the best approach to curtail the menace of the deadly disease, with human migration as the target area of concern.
Rashidat [20], developed a deterministic-stochastic class of fractional order model, to examined the impact of transmission process between infected humans and rodents, finding that incorporating all the transmission processes resulted in high increase of the infection rates. Madubueze [21] developed transmission dynamics of Lassa fever in cooperating death compartment that were capable of transmitting the disease and recommended sensitization establishments of more diagnosis centers and precautionary measures during burial to curtail the menace of Lassa fever. Additionally, other studies [17, 22-24, 16, 25-27, 34 and 39-40], have developed models to evaluate the cost-effectiveness of Lassa fever control measures. Despites these studies, there has no research examining the economic impact of Lassa fever in the North east region of Nigeria. However, in this study, we develop mathematical model to estimate the economic burden of Lassa fever in healthcare system, affected communities and overall economy of Bauchi. The result of this analysis will contribute to the existing body of knowledge on Lassa fever transmission dynamics and offer insights for improving prevention strategies and managing the economic impacts of the disease.
The rest of the work are organized as follows, description of the model is section 2 and Basic properties of the model in section 3, while section 4, is existence and stability of the Lassa fever disease, section 5 is Sensitivity analysis of the threshold, section 6 Numerical Simulation of the threshold, section 7 Discussions, section8 Conclusion.
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